Mersenne: Re : Odd's on finding a factor (part 2)

[Dave Mullen]

Sorry, I'm no mathematician, and new to the Mersenne field.   > No, in the x-y bit range (remember that n bit integers are about 2^n) the first factor could be x/2 to y/2 bits long (powers of a power multiply).   What I was trying to say in my disjointed way was ...   (Example) M11 = 2047 (11 bits long). Now 2047 has only 2 factors (23 x 89) and the square root of 2047 is approx 45. 45 is 6 bits long, therefore the factor lower than the square root must have <= 6 bits, and the factor higher than the square root must have >=6 bits.   23 is 5 bits long, and 89 is 7 bits long.   Thus for the exponent 11650000 bits long, if it only has 2 factors , then the first factor must be between 2 and 3413 bits long, and the second factor must be between 3413 and 11649999 bits long. Note that the bit lengths of the 2 factors added together must equal the bit length of the Prime (or bit length of the Prime + 1) !!   > Abreviate!  Use scientific notation...   Ooops.   > Why are you only setting k==1 mod 2^16? (I'm probably missing something obvious)   Yes, my failure to express myself properly - I meant I test each exponent with all "k" multipliers in the range 1 to 2^16.   > I think under windows that dos windows only run when they are "up".   Under Win 98, they chug along quite happily in the background, unless you're running some other DOS box in Full Screen mode (I think).   > You would probably get better results with Will Edgington's mersfacgmp program, and DJGPP (a port of g++ to dos).   I'll check it out. I'm using UBASIC because for testing factors of large Mersenne, I don't need to actually represent the full Mersenne Prime. If you're familiar with UBASIC try ...   Result = MODPOW(2,MersenneExponent,TrialFactor)   where TrialFactor is the MersenneExponent * 2 * (some k in range 1 to 2^16) + 1.   If Result = 1 then TrialFactor divides the Mersenne Prime. As UBASIC can handle around 2600 decimal digits, in theory (and with a lot of time), I could check all factors up to 2600 decimal digits for any given exponent. It's a damn sight faster than filling 16MB+ of memory with 1's and then trial dividing.