RE: Statistical Analysis of Prime Exponent Mersennes
After much private debate, I'm providing the following I have
inquired and received information about. Please, don't flame
me or ask me to explain further, as I'm only the messenger and
don't have all the answers myself...
Q: Can all the data be posted to the list?
A: HA! Not likely. The current size of 1.43TB of "raw" data
which must be "interpreted" (taking 25+ times the space)
is too large. I don't know about others, but I don't have
the 20+ years to download the data over a 56K modem if
posted to the list...
Q: What algorithms are used?
A: 'A variety of standard algorithms and methodologies used
in traditional and non-traditional statistical analyses.
Used in large number of complex, unique and even 'unusual'
relations.'
Q: Is the code and/or program available?
A: 'No. Major chunks of code are proprietary, licensed,
patented [or pending] or 'otherwise' restricted from
distribution. Typical PC unable to run; Lack of memory
or storage.'
Q: Can you provide data on M727, M751, M#39, M#40, M*10M-digit?
A: 'Here is info.'
ACTUAL (REAL-LIFE INTERPRETED) DATA:
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
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
M#39 - 53.7390% probability - range=10987349-11013853
M#39 - 64.0127% probability - range=10914203-11092621
M#39 - 81.6073% probability - range=10793527-11204183
M#39 - 97.3391% probability - range=10526447-11390453
M#40 - 61.4726% probability - range=13430227-13501387
M#40 - 77.3902% probability - range=13359163-13592549
M#40 - 86.0715% probability - range=13231913-13684399
M#40 - 96.5507% probability - range=13092361-13973117
M#43 - 58.3097% probability - range=41976841-42057331
M#43 - 71.6352% probability - range=41901683-42138559
M#43 - 79.7464% probability - range=41753977-42302809
M#43 - 93.4218% probability - range=41564021-42516373
NOTE: Highly composite means 6 or more factors of the
factor - 1...
Eric
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