65 bit to 66 bit unit time expansion

[Jwb52z]

What's the expansion factor/rate when going from 65 to 66 bits in relation to the time that units take to finish?

[cheesehead]

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:

/* 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 */