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2002-12-20, 07:15   #2

"Richard B. Woods"
Aug 2002
Wisconsin USA

22·3·641 Posts

There are twice as many potential factors between 2^65 and 2^66 as there are between 2^64 and 2^65.

In general, trial factoring from 2^n to 2^n+1 requires about as many trials of potential factors as trial factoring from 2^1 all the way to 2^n. I.e., each increase of 1 in the power-of-2 doubles the total trials requirement up to the power-of-2 limit.

Here's a section of comment in the source code of Prime95 module commonc.c:
Quote:
 /* If factoring, guess how long that will take. Timings are based on */ /* how long it takes my PII-400 to process the exponent 12,000,017. */ /* Below 2^60, prime95 runs through 0.004093*2^58 factors in 3.198 seconds. */ /* Below 2^62, prime95 runs through 0.004093*2^58 factors in 3.204 seconds. */ /* Below 2^64, prime95 runs through 0.004093*2^58 factors in 5.949 seconds. */ /* Above 2^64, prime95 runs through 0.004093*2^58 factors in 13.511 seconds. */ /* Compute timing * 2^limit / (0.004093 * 2^58) * (12,000,017 / p) */ /* Which simplifies to: timing * 2^(limit-44) * 178945.25 / p */