20220327, 02:02  #1 
"Καλός"
May 2018
2×3^{2}×19 Posts 
Recreational Tests
Let's start this recreational thread with tests on base10 exponents ending in countdown sequences:
M97654321 (Verified) M337654321 M467654321 M637654321 M877654321 M947654321 (Factored) Last fiddled with by Dobri on 20220327 at 02:07 
20220328, 05:19  #2 
"Καλός"
May 2018
2·3^{2}·19 Posts 
Golden Ratio

20220329, 03:08  #3 
"Καλός"
May 2018
2×3^{2}×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. 
20220331, 02:07  #5  
"Καλός"
May 2018
2·3^{2}·19 Posts 
Quote:
Let’s also consider exponents with base10 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 20220331 at 02:17 

20220403, 11:53  #7 
Einyen
Dec 2003
Denmark
2·5^{2}·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. 
20220403, 12:35  #8  
"Καλός"
May 2018
2×3^{2}×19 Posts 
Quote:
Here the effort is toward the complete factorization of M1277 in the future by performing consecutive CPRP tests after every new prime factor until eventually reaching a probablyprime PPRP status with no remaining factors to find. Let's consider this trivial CPRP 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 20220403 at 13:06 

20220403, 14:40  #9 
Einyen
Dec 2003
Denmark
110100010110_{2} Posts 
Ok....yeah I'm sure that PRP test helped immensely towards factoring M1277, what a tremendous effort from you.

20220404, 00:26  #10  
Feb 2017
Nowhere
2·3·983 Posts 
Quote:
Nowadays, the PariGP command ispseudoprime(2^12771) 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. 

20220404, 19:23  #11 
"Καλός"
May 2018
2·3^{2}·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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