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Old 2019-12-10, 22:15   #16
ewmayer's Avatar
Sep 2002
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Originally Posted by ATH View Post
Mfactor.exe -m 478923550381407695195061911293 -kmax 100000000
pass = 1.
Factor with k = 18608. Program: E3.0x

The exponent is 98.6 bits and the factor is 113.8 bits.
Found the bug that was hosing my v19/P2WORD run of this one ... fix will be included in next update of the v19 beta tarball, unless someone needs it sooner.

It seems the lowest k-max is 16,336,320 even if you choose a smaller value, so the exponent limit is p< 2^128 / (2*16336320)
Yes, that min-kmax is the number of bits in the small-primes sieve, we always do complete passes through it, not worth adding logic to quit early when the user's requested kmax has been hit.
The highest prime below that value is:

Mfactor.exe -m 10414902711288052127510192241307 -kmax 10000000
pass = 1.
Factor with k = 3668. Program: E3.0x
Exponent 103.0 bits and factor 115.9 bits
With above-noted factor.c fix, v19 finds this as well.

If you allow composite exponents the highest one is: 10414902711288052127510192241329.
M(10414902711288052127510192241329) has 0 factors in range k = [0, 16336320], passes 0-15
"If you allow composite exponents" -- did your v14.1 build accept this without modifications, or did you disable the prime-p check? Because both v14.1 and the current version of factor.c have the same is-PRP check on p, in v14.1 at line 1017 and in v19 at line 1270, and both (I built v14.1 factor just now, just to be sure) throw the same assertion, just from those different line numbers:

Factoring self-tests completed successfully.
p is not prime! Offending p = 10414902711288052127510192241329
ERROR: at line 1273 of file ../factor.c
Assertion failed: 0

If you disabled that check yourself, that's fine, as long as you're OK with just looking for that subset of factors which are of the prime-exponent required form.
Here is a 122.3 bits factor:
Mfactor.exe -m 10104654968465468549684654654563 -kmax 10000000
pass = 14.
Factor with k = 313197. Program: E3.0x
Fixed-up v19 also finds.
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