Thread: My Apologies View Single Post
 2010-08-02, 03:08 #70 lavalamp     Oct 2007 Manchester, UK 53F16 Posts There is a little table on here: http://www.mersenne.org/various/math.php I'll reproduce it here slightly edited: Code:  Exponents Bit up to depth --------- ----- 3960000 60 5160000 61 6515000 62 8250000 63 13380000 64 23390000 65 29690000 66 37800000 67 47450000 68 58520000 69 75670000 70 96830000 71 This relationship between log(exponent) and bit depth is roughly linear, with a bit of a kink around 64 and 65 bits. If you plot the log of the exponent against the bit depth (log to base 2 of the trial factor to depth), you get a nice straight line from a bit depth of 65 onwards. I added a trend line to that and the equation was this: ln(E) = 0.2346*D + 1.7171 Where E is the exponent and D is the bit depth. So using this, it's tentatively possible to extend the table, but whether or not this linear relationship should continue I don't know. Assuming it does, here's what the numbers would be: Code:  Exponents Bit up to depth --------- ----- 23390000 65 29690000 66 37800000 67 47450000 68 58520000 69 75670000 70 96830000 71 120640000 72 152530000 73 192860000 74 243860000 75 308340000 76 389860000 77 492940000 78 623280000 79 788070000 80 996440000 81 1259900000 82 1593020000 83 2014220000 84 2546790000 85 3220170000 86 4071590000 87 So it seems as though Operation Billion Digits should be taking numbers to 87 bits, and currently there are 10 (soon to be 13) exponents that are at 81 bits. Also, the first lot of 100 million digit candidates should be trial factored to 77 bits. Once again, I do not know if this linear relationship between exponent and trial factor depth should continue. So take it with a pinch of salt until someone who actually knows something about it makes a comment. Last fiddled with by lavalamp on 2010-08-02 at 03:10