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Old 2022-03-27, 02:02   #1
Dobri
 
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Default 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
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Old 2022-03-28, 05:19   #2
Dobri
 
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Default 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,...
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Old 2022-03-29, 03:08   #3
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The exponent of the most factored Mersenne number (12 prime factors) to date,

M726064763,

see also https://mersenneforum.org/showthread.php?t=27436.
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Old 2022-03-29, 12:32   #4
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I like the forthrightness and accuracy of the designation "recreational."

See also this post.
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Old 2022-03-31, 02:07   #5
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Quote:
Originally Posted by Dr Sardonicus View Post
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
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Old 2022-04-03, 08:58   #6
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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
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Old 2022-04-03, 11:53   #7
ATH
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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.
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Old 2022-04-03, 12:35   #8
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Quote:
Originally Posted by ATH View Post
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
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Old 2022-04-03, 14:40   #9
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Ok....yeah I'm sure that PRP test helped immensely towards factoring M1277, what a tremendous effort from you.
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Old 2022-04-04, 00:26   #10
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Quote:
Originally Posted by Dobri View Post
<snip>
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.
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Old 2022-04-04, 19:23   #11
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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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