Hi everyone ,I have a number and need some help for it's integer factorization.
The 200 digits number comes from the book "In Code: A Mathematical Journey" written by Sarah Flannery and her father.
Because the author claim that we can't factor this number even with the supercomputer.
But RSA-200,the number almost the same size had already been factored way back in 2005,and a much bigger number RSA-768 which has 232 decimal digits had been factored in 2009.
So I am looking forward to having your kind help in this regard

The 200 digits number from the book "In Code: A Mathematical Journey":
31580479476026838343434028711320725847154882228947750154281522280836834473689746760598075754629059483639555637314474524275903519617611963787093324474266058093181460871296266561056469547820922800384429

Best regards
brianwu21

That book was written a decade ago, a few years before RSA-200 was first factored. Both hardware and software have advanced significantly since then. NFS@Home is certainly capable of factoring a 200-digit GNFS using the lasievef application, but it would require significant time for both the sieving and linear algebra. I cannot justify spending this much of the NFS@Home participants' and supercomputer time for a number that's just a curiosity. Sorry.

That book was written a decade ago, ... I cannot justify spending this much of the NFS@Home participants' and supercomputer time for a number that's just a curiosity. Sorry.

I'm not curious, even. For comparison, the largest GNFS currently on
NFS@Home's list is 183.7. I hear that adding five digits to the size
in GNFS in this range doubles the difficulty (runtime, in particular);
that's three doublings (at a minimun), 8-times as difficult.

Also, I wondered on reading the original post how closely the person
posting had looked at the two numbers referred to, RSA200 and then
RSA768 (at 232-digits, maybe 233?). Both numbers were done by a single
non-public group, with dedicated hardware; a group that includes the
people that wrote the original lasieve code, using completely different
linear algebra code, that I don't believe is yet in the public domain.
The current NFS@Home project on SNFS is the first pass at a public
approach to the records set by that group; Bonn (GNFS200), Bonn-NTT-EPFL
(SNFS1024) then Bonn-NTT-EPFL again (GNFS232) over a decade-or-more's work.
We're just now about to meet, and then break, their SNFS record --- check
the status page --- 2,1031- SNFS 310.7 and 2,1061- SNFS 319.7, respectively.

For a comparable public project on GNFS, mersenneforum may have the best
chance; having recently completed GNFS187, and just starting on GNFS197.
The first attempt at the GNFS matrix failed, after months of computing;
and we were very happy that the second attempt succeeded. A suggestion
that GNFS200 is now on the borderline of being routine, as a public project,
just isn't correct. Finding and multiplying two 100-digit primes is indeed
a plausible project for a computing beginner; hardly even requiring a
math coding prodigy. Breaking 200-digit composites isn't yet in that range.

-bdodson (still NFS@Home's top contributor; first past 50M credits)

I understand that ,and I appreciate all your help and informations.

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