JSH: James Harris Surrogate Factors RSA-100

About ten days ago, James Harris was kind enough to share
with me the latest version of his surrogate factoring program,
written in Java.

James and I agreed that James would refrain from posting to
Usenet until I could generate my results using his program.

With a few minor tweaks, I was able to use James's program to
factor RSA-100 in a little over 172 hours on a 2.4 gigahertz AMD
processor running Linux.

Here is the output from the program:

Example
1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139:

n=1
f_1.mod(p)=259
f_2.mod(p)=483
alpha*k mod(p)=182
alpha^{-1}*(1+a^2)k mod(p)=235

k_0=196616
k=285340
alpha=23

maxPrime=4294967291

k_0/p=317
steps=12

Total all combinations: 4876527219
Time: 44548007
Time/combination: 0.006133562458474485

Surrogate: 42949672954294967295
 (  3 )( 5 )( 17 )( 101 )( 257 )( 3541 )( 27961 )( 65537 )
Product: 42949672954294967295

Surrogate combinations checked: 570889211
Initial Factorization:

f_1=214433
f_2=95527039
Now checking its factors...
Success!
Factors:
 ( 37975227936943673922808872755445627854565536638199 )
( 40094690950920881030683735292761468389214899724061 )
Product:
1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139:

In coming is
1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139:

Surrogate factorization data for target:

Surrogates factored     : 43079822
Surrogates not factored : 91
Factored fuel percentage: 97%

Processing time: 619315203
Number of digits: 100
bitLength=330

I shared this result with James, but with his characteristic
modesty he declined to acknowledge its significance.

Fearing that this could mean the end of human civilization,
James asked me not to publicize the results.  However, I could
not bring myself to contain information this im****tant, nor could
I suppress this obvious vindication of the true, living, super genius
that is James Harris.

True, RSA-100 is the smallest of the RSA challenge numbers,
but it cannot be denied that this is an historic step towards
James's goal of solving the factoring problem.

To further improve run times, I plan to ****t James's code to
the computer languages best known for their performance,
LISP, SNOBOL, and Phrogram.