how are odds computed? - Page 3

Peter Nelson · 2005-10-17, 03:27

Just out of interest, the 1.803 is a constant in the program if the p-1 test has already been completed.

Before the p-1 test is done then the formula used has the alternative constant 1.733. This would also be the case if for some reason you skipped the p-1 test altogether and never ran it.

As an exercise or for your project you might like to run a loop for different values of the bit depth and look at how the odds vary for a given exponent depending on how far your trial factored it.

Peter Nelson · 2005-10-17, 03:47

Here is an example for an exponent I am currently LL testing.

constant: 1.733 1.803

trialfactor without p-1 after p-1
bitdepth 34843141 34843141

32 648570 623390
33 628302 603909
34 609262 585608
35 591343 568385
36 574447 552145
37 558491 536808
38 543396 522299
39 529096 508555
40 515530 495515
41 502641 483127
42 490382 471343
43 478706 460121
44 467573 449420
45 456947 439206
46 446792 429446
47 437079 420110
48 427780 411172
49 418868 402606
50 410319 394389
51 402113 386501
52 394228 378923
53 386647 371636
54 379352 364624
55 372327 357872
56 365557 351365
57 359029 345090
58 352731 339036
59 346649 333191
60 340774 327543
61 335094 322084
62 329601 316804
63 324285 311695
64 319137 306747
65 314151 301954
66 309318 297309
67 304631 292804

This is consistent with the way prime95 calculates odds (I made them integers for readability) and its telling me 1 in 292804 as expected.

This is quoted as an estimate of the probability.

I do not know in fact how accurate the formula is (possibly it is only valid for certain rough exponent size range and may be unsuitable for 100 million digit primes which would be bigger exponents than current testing).

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2005-10-17, 03:27	#23
Peter Nelson Oct 2004 23² Posts	Just out of interest, the 1.803 is a constant in the program if the p-1 test has already been completed. Before the p-1 test is done then the formula used has the alternative constant 1.733. This would also be the case if for some reason you skipped the p-1 test altogether and never ran it. As an exercise or for your project you might like to run a loop for different values of the bit depth and look at how the odds vary for a given exponent depending on how far your trial factored it.

2005-10-17, 03:47	#24
Peter Nelson Oct 2004 23² Posts	Here is an example for an exponent I am currently LL testing. constant: 1.733 1.803 trialfactor without p-1 after p-1 bitdepth 34843141 34843141 32 648570 623390 33 628302 603909 34 609262 585608 35 591343 568385 36 574447 552145 37 558491 536808 38 543396 522299 39 529096 508555 40 515530 495515 41 502641 483127 42 490382 471343 43 478706 460121 44 467573 449420 45 456947 439206 46 446792 429446 47 437079 420110 48 427780 411172 49 418868 402606 50 410319 394389 51 402113 386501 52 394228 378923 53 386647 371636 54 379352 364624 55 372327 357872 56 365557 351365 57 359029 345090 58 352731 339036 59 346649 333191 60 340774 327543 61 335094 322084 62 329601 316804 63 324285 311695 64 319137 306747 65 314151 301954 66 309318 297309 67 304631 292804 This is consistent with the way prime95 calculates odds (I made them integers for readability) and its telling me 1 in 292804 as expected. This is quoted as an estimate of the probability. I do not know in fact how accurate the formula is (possibly it is only valid for certain rough exponent size range and may be unsuitable for 100 million digit primes which would be bigger exponents than current testing).