Recreational Tests
 

Let's start this recreational thread with tests on base-10 exponents ending in countdown sequences:
M[M]97654321[/M] (Verified)
M[M]337654321[/M]
M[M]467654321[/M]
M[M]637654321[/M]
M[M]877654321[/M]
M[M]947654321[/M] (Factored)

Golden Ratio
 

Exponents with base-10 digits close to the golden (1.61803398...) ratio:
M[M]161803337[/M],
M[M]161803339[/M] (Factored),
M[M]161803361[/M] (Factored),
M[M]161803363[/M] (Factored),
M[M]161803387[/M] (Verified),
M[M]161803393[/M] (Factored),
M[M]161803403[/M] (Verified),
M[M]161803409[/M] (Factored),
[FONT=&quot]M[M]161803427[/M] (Factored),[/FONT]
[FONT=&quot]M[M]161803463[/M],...[/FONT]

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

M[M]726064763[/M],

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

I like the forthrightness and accuracy of the designation "recreational." :tu:

See also [url=https://www.mersenneforum.org/showpost.php?p=567248&postcount=6]this post[/url].

[QUOTE=Dr Sardonicus;602793]I like the forthrightness and accuracy of the designation "recreational." :tu:

See also [url=https://www.mersenneforum.org/showpost.php?p=567248&postcount=6]this post[/url].[/QUOTE]
Thanks for the link, it is good to know that some recreational tests may be useful for quality assurance (QA) purposes.:plus:
Let’s also consider exponents with base-10 digits close to the reciprocal ([I]Phi[/I] = 1/[I]phi[/I] = [I]phi[/I] - 1 = 0.618033988...) of the golden ratio:

M[M]61803349[/M],
M[M]61803361[/M] (factored),
M[M]61803383[/M] (factored),
M[M]61803419[/M] (factored),
M[M]61803439[/M] (factored),
M[M]61803451[/M] (verified),
M[M]61803457[/M] (verified),
M[M]61803463[/M] (factored),
M[M]61803473[/M] (factored),
M[M]61803481[/M] (factored),
M[M]61803487[/M] (verified),
M[M]61803571[/M] (factored),
M[M]61803587[/M] (factored),
M[M]61803601[/M] (factored),
M[M]61803607[/M] (factored),
M[M]61803631[/M] (factored),
M[M]61803641[/M] (verified),
M[M]61803659[/M] (verified),
M[M]61803667[/M] (factored),
M[M]61803673[/M],…,

M[M]618033917[/M],
M[M]618033931[/M] (factored),
M[M]618033947[/M] (factored),
M[M]618034003[/M] (factored),
M[M]618034013[/M] (factored),
M[M]618034069[/M] (factored),
M[M]618034097[/M] (factored),
M[M]618034121[/M],...

There is no PRP test in GIMPS for M[M]1277[/M] to date.
Here is my residue: C-PRP 076D5C08E15214[SPOILER]:)[/SPOILER].
[code]
Residue Shift Type
076D5C08E15214__ 153 1
[/code]

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.

[QUOTE=ATH;603184]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.[/QUOTE]
That is correct.
Here the effort is toward the complete factorization of M[M]1277[/M] 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 M[M]1277[/M]... :smile:

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

[QUOTE=Dobri;603186]<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 M[M]1277[/M]... :smile:[/QUOTE]
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.

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 M[M]100000007[/M], and locate remaining tests to be done on exponents containing lots of 0s.

M[M]200000201[/M] (Factored)
M[M]300000031[/M] (Unverified)
M[M]300003001[/M]
M[M]300030001[/M] (Factored)
M[M]300300001[/M] (Factored)
M[M]303000001[/M] (Unverified)
M[M]330000001[/M] (Factored)
M[M]550000001[/M]
M[M]600060001[/M]
M[M]600600001[/M]
M[M]606000001[/M]
M[M]880000001[/M]
M[M]900900001[/M]

For quality assurance (QA) purposes, a stage-1 P-1 test was performed on M[M]726064763[/M] without excluding in quotation marks the 12 known factors.
The result is a 145-digit 481-bit composite factor which is a product of 9 out of said 12 known factors.
[code]
3134690288679616476294198707737821625845346697889718910134714712563252971000595991522674571561096903867990492012061630874233422946354627851588807 = 1452129527 × 1023751315831 × 1030134877226297 × 7106729160891631 × 7236079050549607 × 12965740712769703 × 37915764094923857 × 7565365825277361223 × 10702385060027676180416983
[/code]

Perhaps more P-1 tests could factor [COLOR=Red]at least one[/COLOR] of the remaining unfactored Mersenne numbers for small exponents:
M[M]1277[/M], M[M]1619[/M], M[M]1753[/M], M[M]2267[/M], M[M]2273[/M], M[M]2423[/M], M[M]2521[/M], M[M]2713[/M], M[M]2719[/M], M[M]2851[/M], M[M]3049[/M], M[M]3673[/M], M[M]3691[/M], M[M]3847[/M], M[M]3881[/M], M[M]3919[/M],...

[QUOTE=Dobri;610908]Perhaps more P-1 tests could factor [COLOR=Red]at least one[/COLOR] of the remaining unfactored Mersenne numbers for small exponents:
M[M]1277[/M], M[M]1619[/M], M[M]1753[/M], M[M]2267[/M], M[M]2273[/M], M[M]2423[/M], M[M]2521[/M], M[M]2713[/M], M[M]2719[/M], M[M]2851[/M], M[M]3049[/M], M[M]3673[/M], M[M]3691[/M], M[M]3847[/M], M[M]3881[/M], M[M]3919[/M],...[/QUOTE]

What exactly do you propose to run these with?

[QUOTE=storm5510;610918]What exactly do you propose to run these with?[/QUOTE]
My submitted P-1 tests on M[M]1277[/M] and M[M]1619[/M] were performed with Intel Core i7-7700 @ 3.60GHz and just 16GB RAM. Let's assume that many users have much better computers and more RAM.

[QUOTE=Dobri;610924]My submitted P-1 tests on M[M]1277[/M] and M[M]1619[/M] were performed with Intel Core i7-7700 @ 3.60GHz and just 16GB RAM. Let's assume that many users have much better computers and more RAM.[/QUOTE]

I have the exact same hardware. I should have phrased my question differently. What software, I should have asked? [I]Prime95, gpuowl, Yafu,[/I] for example.

[QUOTE=Dobri;610924]My submitted P-1 tests on M[M]1277[/M] and M[M]1619[/M] were performed with Intel Core i7-7700 @ 3.60GHz and just 16GB RAM. Let's assume that many users have much better computers and more RAM.[/QUOTE]

I did P-1 on M1277 with B1=10[SUP]12[/SUP] and B2=2.35*10[SUP]17[/SUP] with GMP-ECM 7.5 years ago back in January 2015, and I wouldn't be surprised if other people went even further.

I did not turn it into primenet because it would just have broken the Ghz-Days system with a gazillion Ghz-Days.

I also did 2 x P+1 runs on M1277 with B1=5.1*10[SUP]11[/SUP] and B2=5.4*10[SUP]16[/SUP] and B2=7.8*10[SUP]16[/SUP].

[QUOTE=storm5510;610927]I have the exact same hardware. I should have phrased my question differently. What software, I should have asked? [I]Prime95, gpuowl, Yafu,[/I] for example.[/QUOTE]
I am using Prime 95 version P95v30.8b15 for P-1 tests while waiting in anticipation for a stable version of P95v30.9 to run ECM more efficiently.
[QUOTE=ATH;610931]...
I did not turn it into primenet because it would just have broken the Ghz-Days system with a gazillion Ghz-Days.
...[/QUOTE]
That is correct, the Ghz-Days statistics for "Totals Overall" is disproportionate now.

[QUOTE=ATH;610931]I did P-1 on M1277 with B1=10[SUP]12[/SUP] and B2=2.35*10[SUP]17[/SUP] with GMP-ECM 7.5 years ago back in January 2015, and I wouldn't be surprised if other people went even further.
[/QUOTE]

I looked at the details for M1277 a while back and saw where someone had ran a really large P-1. I did not pay attention to when it was completed. If a person includes all the ECM data, it takes a while for it to come up on Primenet. M1277 goes way beyond a "recreational test!"

This one is for the less ambitious lads and gals, a notch below the 332,192,809 100-MDigit threshold, please consider the DC of M[M]332192779[/M].

I'm wondering why there was a need to recheck the trial factoring bits of M[M]161803403[/M] from 2[SUP]73[/SUP] to 2[SUP]78[/SUP]. Kriesel's hardware is very reliable, there wouldn't have been any errors.

[QUOTE=tuckerkao;611890]I'm wondering why there was a need to recheck the trial factoring bits of M[M]161803403[/M] from 2[SUP]73[/SUP] to 2[SUP]78[/SUP]. Kriesel's hardware is very reliable, there wouldn't have been any errors.[/QUOTE]
There is no special reason, often my automated script configures the TF tests listed in a queue to start from the lowest 2[SUP]1[/SUP] value.
As concerned with reliability, the TF tests have no error correction mechanism.
With the limited error correction for LL tests, the quoted user currently has 1563 verified test results and 32 bad test results, see [URL]https://www.mersenne.org/report_ll/?exp_lo=2&exp_hi=999999937&dispdate=1&user_only=1&user_id=Kriesel&B1=[/URL].

Among the 51 prime exponents of known Mersenne primes, there are only 4 remaining exponents (M[M]25964951[/M], M[M]30402457[/M], M[M]37156667[/M], and M[M]57885161[/M]) where a factor is yet to be found for at least one of the Mersenne numbers of either the [COLOR="Blue"]preceding[/COLOR] [COLOR="Red"]or[/COLOR] [COLOR="blue"]succeeding[/COLOR] prime exponents ([COLOR="red"]or[/COLOR] both) excluding the small consecutive prime exponents which give Mersenne primes:
M[M]25964929[/M], M[M]25964957[/M];
M[M]30402401[/M], M[M]30402479[/M];
M[M]37156663[/M], M[M]37156673[/M]; and
M[M]57885143[/M], M[M]57885167[/M].

"Upgraded" martinette from 16GB to 64GB, to run v30.8 P-1, lost reliability, so running PRP on it for now. Can you tell when? [url]https://www.mersenne.org/report_LL/?dispdate=1&user_id=Kriesel&comp_id=martinette[/url]

[QUOTE=kriesel;619609]"Upgraded" martinette from 16GB to 64GB, to run v30.8 P-1, lost reliability, so running PRP on it for now. Can you tell when? [url]https://www.mersenne.org/report_LL/?dispdate=1&user_id=Kriesel&comp_id=martinette[/url][/QUOTE]
From Post #23 (2022-08-23, 1563 verified test results and 32 bad test results) till now (2022-12-13, 1799 verified test results and 45 bad test results), it appears that there were 45 - 32 = 13 new bad test results related to all of your computers as the DC wavefront progresses.

Date sort this gives a 9 day period of uncertainty, 2022-10-15 to 2022-10-24, between all 31 good on martinette before "upgrade" and all 5 bad after. [url]https://www.mersenne.org/report_LL/?dispdate=1&user_id=Kriesel&comp_id=martinette[/url]
(Consulting the Windows system event log shows a boot on 2022-10-22.)

[QUOTE=kriesel;619612]Date sort this gives a 9 day period of uncertainty, 2022-10-15 to 2022-10-24, between all 31 good on martinette before "upgrade" and all 5 bad after. [url]https://www.mersenne.org/report_LL/?dispdate=1&user_id=Kriesel&comp_id=martinette[/url]
(Consulting the Windows system event log shows a boot on 2022-10-22.)[/QUOTE]

Martinette? What is it you are trying to accomplish? :ermm:

[QUOTE=storm5510;619851]What is it you are trying to accomplish?[/QUOTE]

I am similarly confused. I don't like being confused.

Dobri and tuckerkao were discussing my hardware fleet's average reliability. A significant component of the recent error rate turns out to have been caused by putting larger new memory in [B]one[/B] laptop that happens to be named martinette; "upgraded" from 1 16 GB DIMM to 2 32 GIB DIMMs for the purpose of running all large-ram P-1 at or below the first test wavefront, made it too unreliable to run LL or P-1. Examining the GIMPS results for it indicated a stark change in reliability downward in mid October. That aligns with a boot on Oct 22, and IIRC the memory "upgrade". Coincidentally, it recently went off warranty, and the power adapter for it has now failed. Dell...
That one laptop is a few percent of my fleet but contributed a disproportionate 38% of the erroneous primality tests during the period. Identifying and taking action on low reliability hardware is a step on the path to raising reliability of results back up to where it should be.

I think I get what you are doing:

Take Mersenne Prime 2[SUP]31[/SUP] as an example. The first non-Mersenne prime below it is 29 and the next above is 37. You are trying to find factors for these adjoining non-Mersenne primes.

Look at post #24. Those eight numbers have been factored to 2[SUP]76[/SUP]. These could be taken much higher with a decent GPU and [I]mfaktc[/I]. Even if you were able to drop out just one, it would be worth the effort.

Here is an untested prime exponent containing [COLOR="Blue"]2023[/COLOR]: M[M]202362023[/M].

And an exponent corresponding to 3am today, [M]202301023[/M], 2023/01/02/0300, has already been factored.

There are also some possible "date exponents" that could use a factor...
[M]20230303[/M]
[M]20230519[/M]
[M]20230621[/M]

Edit: Reserving them for P-1.

Here are some unique (in a recreational sense) 8-digit prime exponents that would need additional [I]P[/I]±1 tests to find more factors of their Mersenne numbers:
M[M]11111117[/M], M[M]11111119[/M], M[M]22222223[/M], M[M]33333331[/M], M[M]55555559[/M], M[M]66666667[/M], and M[M]88888883[/M].

Here is one more (unique, in a recreational way) 8-digit prime exponent: M[M]23456789[/M].

Some redundant TF tests for software testing and quality assurance (QA): M[M]11[/M], M[M]23[/M] and M[M]29[/M].

[QUOTE=Dobri;629438]Some redundant TF tests for software testing and quality assurance (QA): M[M]11[/M], M[M]23[/M] and M[M]29[/M].[/QUOTE]

Hi,

Could you do the Primenet server admins a favor and [I][B]NOT[/B][/I] submit your test results to the server? Especially, do not hand tweak results and hope they get accepted eventually. :smile:

Thanks. I'm going to remove your most recent results like that.

[QUOTE=Madpoo;629473]Hi,

Could you do the Primenet server admins a favor and [I][B]NOT[/B][/I] submit your test results to the server? Especially, do not hand tweak results and hope they get accepted eventually. :smile:

Thanks. I'm going to remove your most recent results like that.[/QUOTE]

Hello, Madpoo, thank you for noticing this loophole. Of course, please delete the TF for M[M]11[/M], M[M]23[/M] and M[M]29[/M].