A little multiplication exercise

[fivemack]

Why not multiply out

1907145664709063958354268537876114943171 * 2282249079063136761889376337454791894323802478621 * 1327437030532454031084789475205826920108788207304808616927065055833914814194080582426819377847


[the hardware and software state of the art is such that factoring 130-digit general numbers, or 180-digit numbers of sufficiently special shape, takes about a week on a 2007-vintage desktop computer using free software; there are various bits of the software you can tweak which I suspect can get that down to four or five days]

Comments

[randwolf.livejournal.com]

5777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
777777777777777777777777777777777777777777777! Ain't bc wonderful?

[simont]

I presume those three factors are prime, on the grounds that it wouldn't be interesting if they were just products of a whole bunch of smaller prime factors?

So I think the more interesting question, to me, is: how did you find out in the first place that 5 × 10¹⁸⁰ + 7/9 × (10¹⁸⁰-1) was the product of sufficiently few sufficiently large primes to be worth factoring?

[cartesiandaemon.livejournal.com]

Reading this suggests a new factorisation optimisation to me

1. Check for primality
2. Google
3. Factorise