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 2022-03-27, 02:02 #1 Dobri   "Καλός" May 2018 2×32×19 Posts Recreational Tests Let's start this recreational thread with tests on base-10 exponents ending in countdown sequences: M97654321 (Verified) M337654321 M467654321 M637654321 M877654321 M947654321 (Factored) Last fiddled with by Dobri on 2022-03-27 at 02:07
 2022-03-28, 05:19 #2 Dobri   "Καλός" May 2018 2·32·19 Posts Golden Ratio Exponents with base-10 digits close to the golden (1.61803398...) ratio: M161803337, M161803339 (Factored), M161803361 (Factored), M161803363 (Factored), M161803387 (Verified), M161803393 (Factored), M161803403 (Verified), M161803409 (Factored), M161803427 (Factored), M161803463,...
 2022-03-29, 03:08 #3 Dobri   "Καλός" May 2018 2×32×19 Posts The exponent of the most factored Mersenne number (12 prime factors) to date, M726064763, see also https://mersenneforum.org/showthread.php?t=27436.
 2022-03-29, 12:32 #4 Dr Sardonicus     Feb 2017 Nowhere 170A16 Posts I like the forthrightness and accuracy of the designation "recreational." See also this post.
2022-03-31, 02:07   #5
Dobri

"Καλός"
May 2018

2·32·19 Posts

Quote:
 Originally Posted by Dr Sardonicus I like the forthrightness and accuracy of the designation "recreational." See also this post.
Thanks for the link, it is good to know that some recreational tests may be useful for quality assurance (QA) purposes.
Let’s also consider exponents with base-10 digits close to the reciprocal (Phi = 1/phi = phi - 1 = 0.618033988...) of the golden ratio:

M61803349,
M61803361 (factored),
M61803383 (factored),
M61803419 (factored),
M61803439 (factored),
M61803451 (verified),
M61803457 (verified),
M61803463 (factored),
M61803473 (factored),
M61803481 (factored),
M61803487 (verified),
M61803571 (factored),
M61803587 (factored),
M61803601 (factored),
M61803607 (factored),
M61803631 (factored),
M61803641 (verified),
M61803659 (verified),
M61803667 (factored),
M61803673,…,

M618033917,
M618033931 (factored),
M618033947 (factored),
M618034003 (factored),
M618034013 (factored),
M618034069 (factored),
M618034097 (factored),
M618034121,...

Last fiddled with by Dobri on 2022-03-31 at 02:17

 2022-04-03, 08:58 #6 Dobri   "Καλός" May 2018 2·32·19 Posts There is no PRP test in GIMPS for M1277 to date. Here is my residue: C-PRP 076D5C08E15214:). Code: Residue Shift Type 076D5C08E15214__ 153 1
 2022-04-03, 11:53 #7 ATH Einyen     Dec 2003 Denmark 2·52·67 Posts There are 4 LL tests on M1277 which are better than PRP tests. GIMPS only switched to PRP tests because of improved error checking during the test and later because of proofs.
2022-04-03, 12:35   #8
Dobri

"Καλός"
May 2018

2×32×19 Posts

Quote:
 Originally Posted by ATH There are 4 LL tests on M1277 which are better than PRP tests. GIMPS only switched to PRP tests because of improved error checking during the test and later because of proofs.
That is correct.
Here the effort is toward the complete factorization of M1277 in the future by performing consecutive C-PRP tests after every new prime factor until eventually reaching a probably-prime P-PRP status with no remaining factors to find.
Let's consider this trivial C-PRP test as an initial cornerstone, one giant leap for the OP man, one small step for mankind toward the factorization of M1277...

Last fiddled with by Dobri on 2022-04-03 at 13:06

 2022-04-03, 14:40 #9 ATH Einyen     Dec 2003 Denmark 1101000101102 Posts Ok....yeah I'm sure that PRP test helped immensely towards factoring M1277, what a tremendous effort from you.
2022-04-04, 00:26   #10
Dr Sardonicus

Feb 2017
Nowhere

2·3·983 Posts

Quote:
 Originally Posted by Dobri Let's consider this trivial C-PRP test as an initial cornerstone, one giant leap for the OP man, one small step for mankind toward the factorization of M1277...
No. The "cornerstone" of M1277 being proven composite was laid long ago.

Nowadays, the Pari-GP command ispseudoprime(2^1277-1) will return 0 (proving the number composite) in a tiny fraction of a second. So (re)proving M1277 composite has indeed become a merely recreational test.

 2022-04-04, 19:23 #11 Dobri   "Καλός" May 2018 2·32·19 Posts A merely recreational test... that makes one think... about 0, for example, and how it is linked to completeness and quality assurance. The number 1 is sufficient to start counting,... so 0 is a recreational term until an origin (or a reference point) is needed. For the next recreational task, let's start from M100000007, and locate remaining tests to be done on exponents containing lots of 0s.

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