Faster factorization applet

[Maybeso]

Congratulations! 2^12345+1 is correct!

Well Paul, no wonder you couldn't identify the other factors.
You made the silly mistake of thinking I'd built my pretty table without making a cut&paste error.

I guess I left out the truncated digits of the C482 when I started the table,
then appended the digit counts to the first, second, ..., last
- not noticing the table had an entry missing.

I hope you didn't spend too much time hunting a bogus algebraic factor.
Had you eliminated 15*823 as a solution?
Sorry about that,

Bruce

[alpertron]

This is the first factorization of a 90-digit number using the SIQS method on my applet. It was done by Gordon Draper.

Of course its speed is not comparable to programs written in C, and for security reasons, all data must fit on memory (no writes are done to hard disk).

Dario,

Good news. It solved successfully. Here is a copy of the output.

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Top window:

982390 293028 352998 698533 588612 030840 778202 635041 783163 987203 790462 368667 044579 180217 826253 = 744 192797 000978 493566 037087 126095 881826 431793 x 1320 074981 896205 203155 253903 315619 028294 800221 

Number of divisors:  4 

Sum of divisors:  982390 293028 352998 698533 588612 030840 778202 637106 050942 884387 487183 659657 486294 090339 058268 

Euler's Totient:  982390 293028 352998 698533 588612 030840 778202 632977 515385 090020 093741 077676 602864 270096 594240 

Moebius: 1

Sum of squares: a^2 + b^2
a = 980 312147 140207 942520 280938 629198 824893 600237 
b = 146 213498 684999 297714 062239 369896 238498 018422


Bottom window:

Factorization complete in 5d 5h 38m 14s
ECM: 18416711 modular multiplications
Prime checking: 107656 modular multiplications
SIQS: 23861833 polynomials sieved
      384673 sets of trial divisions
      20159 smooth congruences found (1 out of every 71020882 values)
      202323 partial congruences found (1 out of every 7076358 values)
      23407 useful partial congruences


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The ECM took approx 10 hours 20 mins, on the 733mhz (256 mb ram) machine. 

This output came from curve 599 on the p3 500mhz machine (128 mb ram).

SIQS finished in about 5 days 5 hours (approx), with a few singletons and
"50 congruences discarded due to linear dependency" occasions during the
matrix solving stage.

[VJS]

Congradulations alpertron,

Alot of people around here use your applet especially for determining if a p-1 p+1 factor is composite or not, determining what the optimal B1 B2 bounds would have been etc. I think it's a great on-line tool and I use it every week.

I was just wondering if you have considered extending the allowed memory allocation (or a user specified feild) and/or size of the max munber of digits for SIQS now that a 90-digit number has been found (Don't know if this is possible).

Thanks,

A big fan of your applet

[ixfd64]

I factored 320² + 2³²⁰ + 1 just for the heck of it. :P

3 x 47 x 103088011295961779 x 9251599612721298293251233503 x 15883803618117864478133605434921392029680687645881