Mersenne: Re: Odds on finding a factor

[Dave Mullen]

>There only a slight error with your logic... For the exponent 11650000, the root is *not* 3413 bits long, but more like 5825000 bits long. Perhaps you forgot exponents add, not multiply.   Okay, next time I'll open my mouth a little wider, so I can fit both feet inside.   Sorry all, sometimes I put my mouth in gear before my brain is engaged.   >Who needs to? I have code which tries any number up to 2^95 as a factor of a Mersenne number with an exponent up to approx. 600 million, using less than 1 KByte of code space and 32 bytes of data storage. It executes in a time proportional to the logarithm of the exponent - for an exponent around 35 million, it takes approximately 2000 CPU clocks i.e. 4 microseconds per test on a 500 MHz CPU.   My UBASIC is running thus :-   In 36 hours, tested 88855 exponents with all multipliers 1 to 2357. (and found factors for 8860 of the exponents).   88855 exponents x 2358 multipliers = 20952090 tests = 1616 tests per second = 618 microsecs per test on a P133.   Brian, I'd be very interested in a copy of that code, if you'd care to E-Mail it.   Regards   Dave Mullen