Recreational Tests

Dobri · 2022-03-27, 02:02

Let's start this recreational thread with tests on base-10 exponents ending in countdown sequences:
M97654321 (Verified)
M337654321
M467654321
M637654321
M877654321
M947654321 (Factored)

Dobri · 2022-03-28, 05:19

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,...

Dobri · 2022-03-29, 03:08

The exponent of the most factored Mersenne number (12 prime factors) to date,

M726064763,

see also https://mersenneforum.org/showthread.php?t=27436.

Dr Sardonicus · 2022-03-29, 12:32

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,...

Dobri · 2022-04-03, 08:58

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

ATH · 2022-04-03, 11:53

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.

Dobri · 2022-04-03, 12:35

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...

ATH · 2022-04-03, 14:40

Ok....yeah I'm sure that PRP test helped immensely towards factoring M1277, what a tremendous effort from you.

Dr Sardonicus · 2022-04-04, 00:26

Quote:

Originally Posted by Dobri

<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.

Dobri · 2022-04-04, 19:23

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.

2022-03-27, 02:02	#1
Dobri "ม้าไฟ" May 2018 2·3·89 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 "ม้าไฟ" May 2018 2×3×89 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,...

2022-04-03, 08:58	#6
Dobri "ม้าไฟ" May 2018 2·3·89 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

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Prime tests / BPSW tests in various number theory packages	MattcAnderson	MattcAnderson	15	2022-02-16 23:11
Hard recreational math problems	swishzzz	Math	9	2020-11-15 19:44
More P-1 tests	dave_0273	Marin's Mersenne-aries	1	2006-03-23 00:03
AI-slavery / recreational discussion	TauCeti	Soap Box	4	2004-04-07 00:00
Bad LL Tests	outlnder	Lounge	8	2002-10-21 00:12

2022-03-29, 03:08	#3
Dobri "ม้าไฟ" May 2018 534₁₀ 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 13·17·29 Posts	I like the forthrightness and accuracy of the designation "recreational." See also this post.

2022-04-03, 11:53	#7
ATH Einyen Dec 2003 Denmark 6574₈ 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, 14:40	#9
ATH Einyen Dec 2003 Denmark 2²·863 Posts	Ok....yeah I'm sure that PRP test helped immensely towards factoring M1277, what a tremendous effort from you.

2022-04-04, 19:23	#11
Dobri "ม้าไฟ" May 2018 216₁₆ 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.