I fully agree to Phil's observation, and I allowed myself the pleasure of running these calculations to prove it:
(M1) is divisible by 1 (M2) is divisible by 3 (M4) is divisible by 5 (M3) is divisible by 7 (M12) is divisible by 13 (M8) is divisible by 17 (M18) is divisible by 19 (M5) is divisible by 31 (M60) is divisible by 61 (M11) is divisible by 89 <----- 11 (M106) is divisible by 107 (M7) is divisible by 127 (M260) is divisible by 521 (M303) is divisible by 607 (M639) is divisible by 1279 (M734) is divisible by 2203 (M190) is divisible by 2281 (M804) is divisible by 3217 (M4252) is divisible by 4253 (M737) is divisible by 4423 (M4844) is divisible by 9689 (M9940) is divisible by 9941 (M11212) is divisible by 11213 (M9968) is divisible by 19937 (M21700) is divisible by 21701 (M967) is divisible by 23209 <----- 967 (M2781) is divisible by 44497 (M86242) is divisible by 86243 (M6139) is divisible by 110503 (M11004) is divisible by 132049 (M43218) is divisible by 216091 (M378419) is divisible by 756839 (M61388) is divisible by 859433 (M139754) is divisible by 1257787 (M1398268) is divisible by 1398269 (M2976220) is divisible by 2976221 (M1510688) is divisible by 3021377 (M6972593) is divisible by M6972593 (M13466917) is divisible by M13466917 of which 2,3,5,11,7,967,6972593,13466917 is prime. Only M11 and M967 has Mersenne prime factors and a prime exponent. And the bet? For now isn't a little frustrating that M#38 & M#39 doesn't divide numbers lower than themselves? For the low values there's very few possibilities for a 2kp+1 to be constructed, eg.: M7 has 0 chances M11 has 1 chance and that will be 23, M13 has 2: 53 & 79, M17 has 4: 103, 137, 239 & 307 .. M29 has 68 chances (after 32 is removed for lacking primality) but for M13466917 there's gotta be billions of billions Especially to Phil and his personal vendetta against me: Please stop it, it's off topic. If you insist nagging on me then please send that to my e-mail adress, [EMAIL PROTECTED], where I can easily make a rule for it's deletion. I'm here for primes and not a timeconsuming quarrel which I could easily find elsewhere on topic. And I don't have the time to explain other than you have totally misinterpreted my previous letters and turned them upside down, you haven't probably the shortest moment considered that my native language is not english, and I recall for you: "one shouldn't be easily offended". Here is something in danish, see if you understand this: "Det er da utroligt, som du tager p� vej. Hvis du bliver ved s�dan, kommer jeg nok til at anse dig for at v�re et vr�vlehoved, som ingen b�r tage alvorligt." happy hunting Torben Schl�ntz > -----Oprindelig meddelelse----- > Fra: Phil Moore [mailto:[EMAIL PROTECTED]] > Sendt: 4. april 2002 23:53 > Til: [EMAIL PROTECTED] > Emne: Re: 2^967 - 1 > > > There is exactly one other: 2^967 -1 is divisible by the Mersenne > exponent 23209, and 967 is prime. For all other known Mersenne > exponents (except 2, 3, 7, 31, 89, 127, and 23209), the order of 2 is > composite. But I certainly wouldn't want to bet against > finding another > prime example, eventually! > > What do you mean: "What a temper and black mood :-( "? > Look, you may have felt that my original reply to Steve Harris' post > was abrupt and/or rude (although he says he didn't find it > so), but you > have twice posted personal attacks on me to the listserve. By > selectively quoting from the letter I sent only to you and Steve, you > leave the impression that the unquoted part expressed an > angry and dark > mood. If there was anything dark or angry about that letter, it could > only have been your state of mind when you read it. I would > appreciate > it if you would refrain from posting such of your > "observations" in the > future; I am sure I am not alone in noticing that both of these two > posts of yours overstepped the bounds of listserve etiquette. > > Sincerely, > Phil Moore > _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
