George Woltman wrote:
>>M727, the smallest Mersenne number with no known factor, is done.
>>(It was clearly out of reach of ecm.)
>>
>>------- Start of forwarded message -------
>>From: Peter-Lawrence.Montgomery
>>Date: Thu, 30 Aug 2001 03:26:19 GMT
>>
>>C(2,727-)
>>* c219 = prp98.prp128. SNFS Dodson/AKL/CWI
>>* Penultimate prime champion
>>* Runner-up for SNFS difficulty
>>
>>17606291711815434037934881872331611670777491166445300472749449436575622328
171096762265466521858927
>>
>>40099499726183758517891939428601665707063794593443940689888526556802581529
262728143398959743444150539520890742947533452401
>>------- End of forwarded message -------
This result does not surprise ME in the least... Anybody on
the list that saw my post back in July of last year... knows
that from the statistcal anaylsis that was done at that
time... I posted the following for M727:
M727 - 94.3716% probability - 2 factors
M727 - 52.8693% probability - 3 factors
M727 - 6.0014% probability - 4+ factors
M727 - 91.1834% probability - 313-bit min. factor size
M727 - 93.0447% probability - 428-bit max. factor size
M727 - 21.7336% probability - highly composite factors
Now we know that M727 has 2 factors... and the factors are
326 and 426 bits in length, respectively... Preliminary
testing also shows that ( factor - 1 ) is NOT highly
composite (having many, many factors)...
Would anybody care to verify the data I posted back then
for M751 ????
M751 - 83.8467% probability - 2 factors
M751 - 74.2974% probability - 3 factors
M751 - 19.5801% probability - 4+ factors
M751 - 87.2999% probability - 281-bit min. factor size
M751 - 81.0003% probability - 526-bit max. factor size
M751 - 30.1716% probability - highly composite factors
Eric
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