Mersenne Digest Thursday, July 1 1999 Volume 01 : Number 591 ---------------------------------------------------------------------- Date: Tue, 29 Jun 1999 23:21:20 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Mersenne FAQ 1.1 On Tue, Jun 29, 1999 at 04:16:19AM -0400, Lucas Wiman wrote: >I corrected a few typos. I then added 500 more of them when I added the LL >section. The LL section needs major revision, and clarification, especially >the repeating LL part. But it still is nice!! Good work. Let us never ever see the `repeating LL remainder' question again. /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Tue, 29 Jun 1999 18:06:18 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: 10,000,000 digit prime >> The 10,000,000 digit prime would have an exponent of over >> 3010299.956, or 3010300 >> which is found by taking (log 2 * 10,000,000) > Actually, it's log10(2) * 10,000,000, which is a different number. Of > course, since I'm not at home, I can't figure out _that_ number offhand, > but see the posts from some weeks back to get the exact first exponent. The formula for determining the number of digits in Mp is p*log_10(2). Therefore, to find the first one with 10^7 digits, we find ceil(10^7/log_10(2)) which is 33219281. Yes, this is going in the FAQ... - -Lucas Wiman ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Tue, 29 Jun 1999 19:17:19 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Hey! <<I'm keeping my fingers, toes and hairs crossed :-) Just too bad nobody else has participated in my guess-contest... That means I will be the sole winner! Hooray!>> Then, later: <<Hmmm, my guess was at about 6,2 million, but nobody else guessed, so there :-)>> Sorry, but I _also_ submitted a guess for M38. Maybe you didn't see it. I, for the record, guessed that M38 has an exponent in the neighborhood of 6.9 million. You may verify this by checking the Mersenne mailing list archives (which is why I made it a point to post my guess to the list :-D ). I also had two other guesses in that post, namely that we're missing a Mersenne prime in the 4mil range (highly unlikely, actually, or so it seems) and a guess at the size of the decamillion digit Mersenne Prime. <<It hasn't been announced yet... but from what little information that is available, i.e. The Oregonian newspaper article, the exponent must be =at least= 6,643,859.>> Ah, my guess of 6.9 million is still safe. :-D Time will tell. S.T.L. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Tue, 29 Jun 1999 19:27:19 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: PrimeNet Stats Updated At 11:17 PM 6/29/99 +0200, Steinar H. Gunderson wrote: >Then what is the best fit? Exponential? :-) It is slightly parabolic. The good news is that it is trending upward faster than linearly. +----------------------------------------------+ | Jud "program first and think later" McCranie | +----------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Tue, 29 Jun 1999 23:46:17 +0000 From: "David L. Nicol" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Mersenne 3/2 conjecture Aaron Blosser wrote: ~> expressions just look much cooler if you throw in a pi Hmm... pi pi pi pi pi pi ( ---- + ---- + ---- ) ** ( ---- + ---- ) + ---- pi pi pi pi pi pi _______________________________________________________________________ David Nicol 816.235.1187 UMKC Network Operations [EMAIL PROTECTED] "on a 80x24 character cell terminal in a damp basement, under a bare light bulb, perched atop a backless wooden stool." ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Tue, 29 Jun 1999 17:26:08 -0700 From: Rudy Ruiz <[EMAIL PROTECTED]> Subject: Mersenne: Re: Mersenne Digest V1 #590 - --------------88161F17489D3CEBF849D8CE Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Date: Mon, 28 Jun 1999 19:45:11 -0700 From: Eric Hahn <[EMAIL PROTECTED]> Subject: RE: Mersenne: A few questions >How large will the exponent be for a 10,000,000 digit prime number? To be a 10,000,000 digit prime number the exponent must be at least 33,219,281 (which also happens to be a Mersenne candidate). >Has the prime number that was found a week ago been announced on this >list? >I.E. What number was it? It hasn't been announced yet... but from what little information that is available, i.e. The Oregonian newspaper article, the exponent must be =at least= 6,643,859. Eric Eric: Isn't 7 million bits something very near to 2^7,000,00 ? I think that could be the case. So could we say: exponent at least 6,900,000? Rudy >From the "The Oregonian" article: The new number is 7 million bits of information -- or more than twice as long. - --------------88161F17489D3CEBF849D8CE Content-Type: text/html; charset=us-ascii Content-Transfer-Encoding: 7bit <!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> Date: Mon, 28 Jun 1999 19:45:11 -0700 <br>From: Eric Hahn <[EMAIL PROTECTED]> <br>Subject: RE: Mersenne: A few questions <p>>How large will the exponent be for a 10,000,000 digit prime number? <p>To be a 10,000,000 digit prime number the exponent must be at least <br>33,219,281 (which also happens to be a Mersenne candidate). <p>>Has the prime number that was found a week ago been announced on <br>this <br>>list? <br>>I.E. What number was it? <p>It hasn't been announced yet... but from what little information <br>that is available, i.e. The Oregonian newspaper article, the <br>exponent must be =at least= 6,643,859. <p>Eric <br> <p>Eric: Isn't 7 million bits something very near to 2^7,000,00 ? <p>I think that could be the case. So could we say: exponent at least 6,900,000? <p>Rudy <p>From the "<i>The Oregonian"</i> article: <p><i>The new number is 7 million bits of information -- or more than</i> <br><i>twice as long.</i> <br><i></i> <br><i></i> </html> - --------------88161F17489D3CEBF849D8CE-- ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Tue, 29 Jun 1999 19:54:58 -0700 From: Eric Hahn <[EMAIL PROTECTED]> Subject: Mersenne: Re: Mersenne Digest V1 #590 >>>Has the prime number that was found a week ago been announced on >>>this list? >>>I.E. What number was it? >>It hasn't been announced yet... but from what little information >>that is available, i.e. The Oregonian newspaper article, the >>exponent must be =at least= 6,643,859. >>Eric >Eric: Isn't 7 million bits something very near to 2^7,000,00 ? >I think that could be the case. So could we say: exponent at least >6,900,000? >Rudy >From the "<italic>The Oregonian"</italic> article: <italic>>The new number is 7 million bits of information -- or more than</italic> <italic>>twice as long.</italic> Good point. But 7,000,000 bits =is= 2^7,000,000 - 1 (which is obviously a composite number) I was looking at the following portion of the article... 'Confirmed this week by George Woltman, a Florida engineer and founder of the "Great Internet Mersenne Prime Search," the new prime possesses more than 2 million digits -- more than twice as many as the previously largest-known prime, which was discovered last year by a 19-year-old college student.' <<pardon the sarcasm!> Whatever the case, certain individuals who have decided to "poach" exponents to ensure M(36) and M(37) are actually M(36) and M(37) respectively, are going to have to wait a loooong time to verify whether this new find is actually M(38) or really M(39), etc. instead. Guess they better get out those Pentium XV 1000GHz processors we heard about earlier. They'll need them to process the well over 35,000 LL tests (including double-checks) to accomplish this task!!! <<ending sarcasm mode> ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Tue, 29 Jun 1999 22:32:08 -0500 From: Ken Kriesel <[EMAIL PROTECTED]> Subject: Mersenne: M38 guess Make my guess for M38, p~=6,740,000 Ken ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 00:44:12 -0500 From: Ken Kriesel <[EMAIL PROTECTED]> Subject: Mersenne: Re: digits vs exponents FAQ At 09:09 AM 1999/06/29 -0400, Jud McCranie <[EMAIL PROTECTED]> wrote: >At 04:16 AM 6/29/99 -0400, Lucas Wiman wrote: >>All, >>Here is version 1.1 of the FAQ. > >Here's a question that needs to be addressed: how to go from digits to >exponents, and exponent to digits. By all means include it in the faq; there's been too much repetition, including wrong responses, now and in past months. Here's a draft: Sometimes it is useful to know the relationship between the exponent of a mersenne number and the number of digits it has in some number base. How do we calculate in either direction? (q) How many digits are there in the binary representation of 2^n-1 (or any number 2^(n-1) <= x <= 2^n - 1) ? (a) n Examples: n=1, 2^(1-1)=2^0=1= 1(2); 2^1-1= 1 = 1(2). n=2, 2^(2-1)=2^1=2= 10(2); 2^2-1= 3 = 11(2). n=3, 2^(3-1)=2^2=4= 100(2); 2^3-1= 7 = 111(2). n=4, 2^(4-1)=2^3=8=1000(2); 2^4-1= 15 = 1111(2). Hey, a pattern's emerging here. (q) How many digits are there in the hexadecimal representation of 2^n-1? (a1) int((n+3)/4) (a2) take the number of binary digits, divide by 4, then round up. (q) How many digits are there in the decimal representation of 2^n-1 ? (a) D = int(n * log_10_(2) + 1); log_10_(2) ~= 0.301029995664 = log (base 10) of 2 Examples: n=1, int(1* .3010... + 1) = 1; n=2, int(2* .3010... + 1) = 1; n=3, int(3* .3010... + 1) = 1; n=4, int(4* .3010... + 1) = 2; ... n=10, 2^n-1=1023; int(10*.3010...+1) ~= int(4.01029995664) = 4; n= 3321925, int(3321925* .3010...+1) ~= int(1000000.068346) = 10^6 n= 33219281, int(33219278* .3010...+1)~= int(10000000.1123) = 10^7 n= 332192807,int(332192807*.3010...+1)~=int( 100000000.2508)= 10^8 n= 3321928095,int(3321928092*.3010..+1)~=int(1000000000.131)= 10^9 (q) What about in some arbitrary number base? (a) For base a as in arbitrary, 2^n -1 will have r digits where r=int(n*log_a_(2) + 1-epsilon), or rather r=ceil(n*log_a_(2)) (allowing for the base a to possibly be a prime number), Example: a=7, n=3, log_2_(7)~= 2.807354922058; log_7_(2)~= 0.356207187108 2^3-1= 7 = 10(base 7) Derivation: 2^n-1 <= a^r-1 or it won't fit in r digits in base a 2^n <= a^r n * log_a_(2) <= r (q) What is the minimum exponent n for 2^n - 1 to have at least D decimal digits? (a) 2^n-1 > 10^(D-1) -1 2^n > 10^(D-1) n > log_2_( 10^(D-1) ) n > log_2_(10) * (D-1); log_2_(10) ~= 3.321928094887 Examples: D=1, n> log_2_(1); n> 0 D=2, n> log_2_(10); n> 3.321...; 2^4-1=15; 2^3-1-7 D=3, n> log_2_(100); n> 6.642...; 2^7-1=127; 2^6-1=63 D=10, n> log_2_(10)*9; n> 29.897... 2^30=1,073,741,824 D=100, n> log_2_(10)*99; n>328.87.. 2^329= 1.093625362392e+99 D=1000, n>3318.6 D=10000, n>33215.95 D=100,000, n>332189.48 D=1,000,000, n> 3321924.772959 D=10,000,000, n> 33219277.62694 D=100,000,000, n> 332192806.1668 D=1,000,000,000, n> 3321928091.565 Ken ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 07:26:55 +0100 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: LL & Factoring DE Crediting On 29 Jun 99, at 23:13, Steinar H. Gunderson wrote: (in reply to my message) > >I agree. However, to take the point to a ridiculous extreme, finding > >a factor saves running a LL test - so why can't I have credit for > >finding 54,522 (small) factors in the range 33.2 million to 36 > >million, thus saving (very approximately) 54,522 * 8 P90 CPU years LL > >testing? The job ran in an hour on a PII-350! > > I'm sure that if you asked Scott, he would credit that to you as factoring > work. Nah, it would be manually submitted results, therefore not eligible. Who cares, anyway? > > However, while a factor `saves' an LL test, this is expected behaviour, > and not something extraordinary. If every factor was going to be credited > as a full LL test, most people would do factoring only! I belive PrimeNet's > solution on this is close to optimal. > Precisely my point. > >(a) you should lose _double_ credit for a LL test if the result is > >proved incorrect, or if a factor is found in a range which you claim > >to have checked; > > Why? I'd rather stick with the PrimeNet policies, where you never lose > any credit at all. To discourage people from generating 20% extra results, mostly bad, by overclocking their systems to a dangerous level instead of being "conservative" & generating reliable results. This would also make it counterproductive to submit "faked" results, therefore allowing credit to be given for results submitted manually. I accept that we all have personal views on this; Scott & George produce different but broadly consistent data, so perhaps it doesn't matter too much. In any case, it's not sensible to "change the rules during the game", unless there's an overwhelming reason for doing so. Regards Brian Beesley ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 07:26:55 +0100 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: 10,000,000 digit prime On 29 Jun 99, at 18:06, Lucas Wiman wrote: > Therefore, to find the first one with 10^7 digits, we find ceil(10^7/log_10(2)) > which is 33219281. NO! The _correct_ formula is ceil((10^7-1)/log_10(2)) = 33219278. The point is that 2^n have 1 decimal digit for n < 4 ;-) As it happens, 33219278, 33219279 & 33219280 are all composite and therefore are not contenders for generating a Mersenne prime. 33219281 _is_ prime, the status of 2^33219281 is (so far as I know) not known at this time ... unless someone found a factor bigger than my 2^40 search limit. Regards Brian Beesley ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 03:05:38 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Mersenne: distribution of factors (was 10,000,000 digit prime) > NO! The _correct_ formula is ceil((10^7-1)/log_10(2)) = 33219278. Aww, mine was pretty close ;-) > The point is that 2^n have 1 decimal digit for n < 4 ;-) > As it happens, 33219278, 33219279 & 33219280 are all composite and > therefore are not contenders for generating a Mersenne prime. > 33219281 _is_ prime, the status of 2^33219281 is (so far as I know) > not known at this time ... unless someone found a factor bigger than > my 2^40 search limit. Well, I don't think that 2^33219281 is prime (factors 1, and 2) :-). But 2^33219281-1 has no factor less than 2^52. No I am not searching in this range, but I made a made this a special case. I am currently searching between 2^47, and 2^50. Which should take almost two more months (unless I find a load of factors, that should make things go faster :) In that range, I an finding about 5.5% to have factors. If this holds, that would be about 3970 new factors, added on to all the other factors that I've found, that makes 19868 factors, less than half of those less than 2^40, despite the fact that the range I tested is 1023 times larger. I realize this is probably a FAQ, (and I intend to put it there), why is the distribution of factors so non-linear? - -Lucas Wiman ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 11:28:00 +0200 From: Alex Kruppa <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: 10,000,000 digit prime > 33219281 _is_ prime, the status of 2^33219281 is (so far as I know) > not known at this time ... unless someone found a factor bigger than > my 2^40 search limit. I tried up to 46695341939693537 ~= 2^55, but no factor. Ciao, Alex. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 07:43:33 -0400 (EDT) From: "St. Dee" <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 guess On Tue, 29 Jun 1999, Ken Kriesel wrote: > Make my guess for M38, p~=6,740,000 I'll guess p~=6,740,001 :-) Kel ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 15:05:07 +0200 From: "Lars Lindley" <[EMAIL PROTECTED]> Subject: SV: Mersenne: M38 guess > On Tue, 29 Jun 1999, Ken Kriesel wrote: > > > Make my guess for M38, p~=6,740,000 > > I'll guess p~=6,740,001 :-) > > Kel I would like anyone betting on M38 tu use an exact exponent! Not ~= blahblah If u dont know any exact exponents, then check http://www.entropia.com/primenet/cleared.txt and pick one there that could be close... You wont be able to see the exact exponent of M38 of obvious reasons, but it can give you an idea... Regards, /Lars ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 09:10:01 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: distribution of factors (was 10,000,000 digit prime) At 03:05 AM 6/30/99 -0400, Lucas Wiman wrote: >I realize this is probably a FAQ, (and I intend to put it there), why is >the distribution of factors so non-linear? Because small factors are more likely to divide a given number. +----------------------------------------------+ | Jud "program first and think later" McCranie | +----------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 10:01:07 -0500 From: "Willmore, David" <[EMAIL PROTECTED]> Subject: RE: Mersenne: M38 guess > > > Make my guess for M38, p~=6,740,000 > > > > I'll guess p~=6,740,001 :-) > > > > Kel > > I would like anyone betting on M38 tu use an exact exponent! > Not ~= blahblah > If u dont know any exact exponents, then check > http://www.entropia.com/primenet/cleared.txt > and pick one there that could be close... > You wont be able to see the exact exponent of M38 of obvious reasons, > but it can give you an idea... > Or, at least pick a prime exponent! :) Come on, Ken, 6,740,000 is *even*. :) Cheers, David ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 19:45:11 +0100 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Re: digits vs exponents FAQ On 30 Jun 99, at 0:44, Ken Kriesel wrote: > >Here's a question that needs to be addressed: how to go from digits to > >exponents, and exponent to digits. > > By all means include it in the faq; there's been too much repetition, > including wrong responses, now and in past months. Actually, things are a great deal easier than Ken makes out. Notation used, square brackets means the "integer part of". I don't like the notation "int(x)" since this has different interpretations in different languages - does it mean chop to zero, chop down or round to nearest or even? "ceil(x)" and "floor(x)" are precise, but meaningless to C non-programmers. Let k be the logarithm of r to base 2. Note that 2^p has [p/k] + 1 digits when represented in base r. k can be calculated as log(r)/log(2) using logarithms to any arbitary base. (a) If k is not a integer (i.e. r is not an integer power of 2), 2^p-1 has the same number of digits as 2^p, because there can be no integers a, b such that a^b = 2^p unless a is an integer power of 2. (b) If k is an integer (i.e. r is an integral power of 2), subtract 1 from the number of digits in 2^p, provided that k divides p. The reverse algorithm (getting the smallest exponent with n digits) is actually even easier: p = [(n-1)*k] + 1 is the smallest p such that 2^p-1 has n digits when represented in base r. (This works only for n > 1 because 2^0-1 = 0 still has 1 digit). Note, the above is actually true irrespective of the numerical value of the symbol "2" - i.e. replace "2" by "3" in the arguments above, and they still work! Regards Brian Beesley ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 22:29:32 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 guess On Wed, Jun 30, 1999 at 07:43:33AM -0400, St. Dee wrote: >I'll guess p~=6,740,001 :-) I'd recommend using a prime, but that's your problem, of course. Well, nobody has gone _over_ your guess, so it probably doesn't matter. (In all other case, choosing the highest non-checked prime above 6,740,000 would have been better.) /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 18:21:58 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Mersenne: Re: M#38 and a few questions Hi all, At 04:02 PM 6/27/99 -0400, Jeff Woods wrote: >Because of >the EFF award money rules, we "GIMPS at large" will not be permitted to >know what the exponent was, or who discovered it, until an article has been >published in a peer-review academic research magazine or such. The EFF rules have been clarified such that if two claims are made on the $50,000 award, then the discovery date determines the winner. This gives us plenty of protection in announcing the new prime now. Scott gave out the press release today to the San Jose Mercury News and I should be emailing the list and updating my web pages soon. Note that sometimes these "human interest" type stories are held until the weekend for publication. I'd like to thank everyone for their patience while any kinks were worked out in the EFF claims process. They have never said we couldn't announce the new prime, but I've held off until we were sure it was risk-free to do so. >>Slowinski used to test huge numbers of primes...is he still doing that? David Slowinski is no longer working for Cray, so I doubt that he is still orchestrating an organized search. GIMPS does have one member who uses Slowinski and Gage's program and a Cray to look for primes. The latest prime is being verified by him. Paul Gage, who still does work for Cray, can then backup the new find. Regards, George ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 03:24:58 +0200 (MET DST) From: [EMAIL PROTECTED] Subject: Mersenne: SF Examiner story Page A-12 of the June 30, 1999 San Francisco Examiner has a story `Math expert confirms a prime discovery' repeating the Oregonian story abut M38. The report does not give the precise exponent. The report mentions only George Woltman by name. Peter ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 19:43:27 -0700 From: Luke Welsh <[EMAIL PROTECTED]> Subject: Mersenne: Is M38 in Seattle Times ? Anybody in the Seattle area? "front section, page 3 of Seattle Times." of a recent edition? Online search fails. - --Luke ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 14:02:35 +1000 From: Simon Burge <[EMAIL PROTECTED]> Subject: Mersenne: M38 I notice that there's a page on the net somewhere that lists M38. I take it that this isn't meant to be public information yet? The page belongs to a previous record holder... Simon (guessing around 6972???, but then I know now :-). ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Wed, 30 Jun 1999 21:24:32 -0700 From: "Joth Tupper" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Is M38 in Seattle Times ? Yup. Page 3, section A, of Tuesday, June 29, 1999 edition of the Seattle Times. "Largest prime ever weighs in at more than 2 million digits" by Ruth Bennett, Newhouse News Service. Perhaps the most significant additions(and I may have simply overlooked these) to the online article (URL already posted) are: a few details about the discoverer (a Ford Motor company employee) and the observation that the previous record prime (about 0.9 million digits) would, if printed in 12 point type, stretch almost 2.5 miles. Does that mean that M38 is the first known 12pt 5 mile prime? Joth - ----- Original Message ----- From: Luke Welsh <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, June 30, 1999 7:43 PM Subject: Mersenne: Is M38 in Seattle Times ? > Anybody in the Seattle area? > > "front section, page 3 of Seattle Times." of a recent edition? > Online search fails. > > --Luke > > ________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 02:21:21 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 >The page belongs to a previous record holder... Took me about 30 seconds to find it. It's nice to see a thirty-eighth line in /root/math/ref/mers... - -Lucas Wiman ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 11:44:20 -0700 From: Lang Pal <[EMAIL PROTECTED]> Subject: Re: Mersenne: Mersenne 3/2 conjecture I have thought very much over your columns and perceived the following: If I replace into the first column the log of (arctan (Mersenne prime exponents)^their index) instead of your first column,(i.e log of (3/2)^n) and the second column remains the same, then you receive a correlation coeficient = 0.9969136, because the limes of arctan (any great number) is PI/2. What is your opinion? Is it false? Best regards Paul La'ng Budapest, Hungary Jud McCranie wrote: > If you take the following comma delimited file into a spreadsheet, and > graph it (say with a line chart) it shows the relationship of Mersenne > exponents to their index, for the first 37 Mersenne primes. The first > column is the log of (3/2)^n, the second column is the log of the exponent > of the nth Mersenne prime. > > ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 05:48:22 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Mersenne: More on the FAQ All, I've done a bit more work on the FAQ, I added the two responses Brian sent. I also broke it up into sections: 1 - introductory stuff 2 - The LL test 3 - Factoring and sieving 4 - Mersenne prime and factor distribution 5 - FFT and DWT 6 - History and Who cares As the FAQ has grown to 14k, I will conserve our bandwidth, it is available at http://www.tasam.com/~lrwiman/FAQ-mers for any who care to read it. Section one is pretty well covered (I might add something about nomeclature), as are sections 2 and 3. In section 4 I need a fair amount of information on mersenne prime distribution, and whether or not there are an infinity of mersenne primes. I don't know if section 5 will ever get written, or if it needs to be. If it does get written it probably won't be by me, since I don't know enough about such things. I think that with the aid of Luke's and Chris Caldwell's sites I should be able to do this pretty easily. - -Lucas Wiman ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 12:22:46 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 At 02:21 01.07.99 -0400, Lucas Wiman wrote: >>The page belongs to a previous record holder... >Took me about 30 seconds to find it. >It's nice to see a thirty-eighth line in /root/math/ref/mers... I didn't! Am I _that_ bad at searching the web? I looked at Gordon's page and Roland's page (found nothing), but couldn't find Joel's page. Help! :-) /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 05:31:00 -0500 (CDT) From: Chris Caldwell <[EMAIL PROTECTED]> Subject: Re: Mersenne: More on the FAQ On Thu, 1 Jul 1999, Lucas Wiman wrote: > All, > I've done a bit more work on the FAQ, I added the two responses I'd strongly suggest using the strength of the web and connecting many of the answers to the fuller explanations already on the web. E.g., those you mention using (or planing to use) below without reference in your draft. (I assume you'll do this eventually, but sometimes it is easier to collect references while drafting.) > of mersenne primes. I don't know if section 5 will ever get written, or > if it needs to be. If it does get written it probably won't be by me, since > I don't know enough about such things. I think that with the aid of Luke's > and Chris Caldwell's sites I should be able to do this pretty easily. For the distribution of primes see the new page http://www.utm.edu/research/primes/notes/faq/NextMersenne.html which briefly discusses the Wagstaff/Lenstra/Pomerance e^gamma conjecture. Chris Caldwell ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 07:17:23 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 >>>The page belongs to a previous record holder... >>Took me about 30 seconds to find it. >>It's nice to see a thirty-eighth line in /root/math/ref/mers... >I didn't! Am I _that_ bad at searching the web? I looked at Gordon's page >and Roland's page (found nothing), but couldn't find Joel's page. You aren't searching for the right people. He didn't say it was a *GIMPS* record holder. You've just gotta know where to look. >Help! :-) All right, here's a hint: he held the record for largest prime, which was also a non-mersenne prime. Check the largest prime by year... - -Lucas Wiman ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 13:22:07 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 At 07:17 01.07.99 -0400, Lucas Wiman wrote: >All right, here's a hint: he held the record for largest prime, which was also >a non-mersenne prime. Check the largest prime by year... David `Mr. Cray' himself? :-) /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 13:26:00 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 At 07:17 01.07.99 -0400, Lucas Wiman wrote: >You aren't searching for the right people. He didn't say it was a *GIMPS* >record holder. You've just gotta know where to look. Found it -- 2^6972593-1 :-) Well, finding that in 30 seconds must mean you knew it was there, or you were incredibly lucky... Does George know about this? /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 08:32:51 -0300 (EST) From: "Nicolau C. Saldanha" <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 On Thu, 1 Jul 1999, Steinar H. Gunderson wrote: > At 02:21 01.07.99 -0400, Lucas Wiman wrote: > >>The page belongs to a previous record holder... > >Took me about 30 seconds to find it. > >It's nice to see a thirty-eighth line in /root/math/ref/mers... > > I didn't! Am I _that_ bad at searching the web? I looked at Gordon's page > and Roland's page (found nothing), but couldn't find Joel's page. > > Help! :-) Try the other record holders, there are not too many of them. You can find links to their home pages at www.mersenne.org. http://www.mat.puc-rio.br/~nicolau ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 13:37:05 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 At 08:32 01.07.99 -0300, Nicolau C. Saldanha wrote: >Try the other record holders, there are not too many of them. >You can find links to their home pages at www.mersenne.org. >http://www.mat.puc-rio.br/~nicolau Don't worry, I've found it already. Looks like I lost the guessing game... /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 08:04:22 -0400 (EDT) From: Lucas Wiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 > Found it -- 2^6972593-1 :-) > Well, finding that in 30 seconds must mean you knew it was there, or you > were incredibly lucky... Does George know about this? Lucky. I went to yahoo.com and typed in 38th, and then stopped. I realized that I should look for the record holders, and through some obnoxious bit of trivia that my brain doesn't let go of I happened to have his URL memorized. Well either that or I am *SEARCHER SUPREME*, but then I would have been the first to find it, on Landon's site. I would assume that George would know since he probably gave the exponent to him in the first place. - -Lucas Wiman ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 14:06:49 +0200 From: "Hoogendoorn, Sander" <[EMAIL PROTECTED]> Subject: RE: Mersenne: M38 Took me a bit longer but has M38 has 2098960 digits ;-) At 02:21 01.07.99 -0400, Lucas Wiman wrote: >>The page belongs to a previous record holder... >Took me about 30 seconds to find it. >It's nice to see a thirty-eighth line in /root/math/ref/mers... I didn't! Am I _that_ bad at searching the web? I looked at Gordon's page and Roland's page (found nothing), but couldn't find Joel's page. Help! :-) /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 14:38:54 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: RE: Mersenne: M38 At 14:10 01.07.99 +0200, Hoogendoorn, Sander wrote: >Try Landon Curt Noll Yes, I tried it after I send that message. The exponent is hardly secret now that even I can find it :-) /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 12:06:56 -0400 From: Jeff Woods <[EMAIL PROTECTED]> Subject: Mersenne: M39 (yes, 39) Very well -- I will now predict that the NEXT Mersenne prime we find will be discovered very shortly (within 60 days, sans verification time), and will be PRECISELY: 2^7682383 - 1 I say this only because I have that number reserved, and because it falls within the subjective "Mersenne Island" that p=6972593 makes possible. (If you take the LARGEST Mersennes, M30 and up, and calculate the gap between them, you will find that the percentage is .8806259 through .9850544. Thus, if I arbitrarily choose 87% either way from the current discovery, this gives an "Island" potential (if such exists) of another prime possibly between p = 6066155 and p = 7879030. I choose to guess that this is the lower of the two primes in this island, if it exists, SOLELY because I'm too stink'n proud to think I might have missed out on the discovery of a WORLD RECORD find. ;-) Now, of course, most of you think the Island theory is bunk. Some of you think it may be conjecture. We'll find out if the THEORY (first put forth by Curt Noll, IIRC) holds for this find. At 01:37 PM 7/1/99 +0200, you wrote: >At 08:32 01.07.99 -0300, Nicolau C. Saldanha wrote: > >Try the other record holders, there are not too many of them. > >You can find links to their home pages at www.mersenne.org. > >http://www.mat.puc-rio.br/~nicolau > >Don't worry, I've found it already. Looks like I lost the guessing game... > >/* Steinar */ > > > >________________________________________________________________ >Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 12:20:51 -0400 From: Jeff Woods <[EMAIL PROTECTED]> Subject: Re: Mersenne: M38 At 08:04 AM 7/1/99 -0400, you wrote: >Well either that or I am *SEARCHER SUPREME*, but then I would have been >the first to find it, on Landon's site. > >I would assume that George would know since he probably gave the exponent >to him in the first place. There is a very short list of people that PrimeNet notifies when a potential prime is found. Scott K, George W, and several past record holders, along with Chris Caldwell (since he maintains the list of known primes). I think Will Edgington is on that list as the pre-eminent factorer among us, but of that I'm not certain. I think Luke may have been there, too -- not sure about that, either. The list was published in a newsletter or FAQ, or perhaps in the documentation for the program.... I'm not sure where I saw this, but I did see it. Curt Noll is in this group. I am not. Yet. ;-) ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ End of Mersenne Digest V1 #591 ******************************
