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Old 2019-03-13, 04:49   #11
mathwiz
 
Mar 2019

7F16 Posts
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Interestingly, GMP-ECM only seems to use gwnum_ecmStage1() if the input is written out explicitly in (2^n +/- 1)/d form, as opposed to a full decimal. E.g.:

Code:
Input number is 7124875134919416452774071346240764917465050401053729788475829418006792633070197260773480462000925038600888030166963314178711084227927169505054967049906157236644045588489318562381444403587801123276191390920852492526599174604254696368010876509960456095578194840205874002033519141134093531142804832239163228700607998501023572045880402900991 (337 digits)
Did not find a gwnum poly for the input number.
Using special division for factor of 2^1243-1
but

Code:
Input number is (2^1243-1)/(2^113-1)/2047 (337 digits)
Found number: 1*2^1243 + -1
Using special division for factor of 2^1243-1
Using B1=850000000, B2=15892628251516, polynomial Dickson(30), sigma=0:10702604903946832294
dF=524288, k=5, d=5705700, d2=17, i0=132
Expected number of curves to find a factor of n digits:
35	40	45	50	55	60	65	70	75	80
15	47	168	661	2867	13623	69471	381778	2221086	1.4e+07
Using gwnum_ecmStage1(1, 2, 1243, -1, 850000000, 1)
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