P-1 on OBD candidates

[clowns789]

Hi Ken, if necessary I can post my server specs again to get it qualification completed, or at least note that it is also an ECC system and all current P-1 assignments are using ECC RAM.

[kriesel]

Originally Posted by clowns789

Hi Ken, if necessary I can post my server specs again to get it qualification completed, or at least note that it is also an ECC system and all current P-1 assignments are using ECC RAM.

Qualifying as I laid it out involves being able to reproduce known factors, and to show run time scaling consistent with completion of good bounds OBD P-1 within 1-2 years solo. By now you have lots of iterations at OBD stage 1 to establish ~192M fft length iteration times. Some small ones (run to mersenne.ca lookup gpu72 row bounds) from https://www.mersenneforum.org/showpo...8&postcount=31 would be quick to run. Stage 2 would need ~64 GiB at OBD. ECC is one element of reliability but an errant CPU could make it miss a known factor.

[kriesel]

Current TF & P-1 status is shown at https://www.mersenne.ca/obd. Current indicated Level is 24.05.
3321928171 TF completed to 92 bits, 2022-02-05 by mersenne.ca user johnny_jack, reserved for P-1, stage 2 5% complete
3321928307 TF completed to 92 bits, 2022-02-23 by kriesel; reserved for P-1, stage 2 ~14% complete on an ECC ram system
3321928319 TF completed to 92 bits, 2022-02-26 by kriesel; reserved for P-1, stage 2 ~16% complete on an ECC ram system
3321928373 TF completed to 92 bits, 2023-02-23 by kriesel; right to reserve P-1 by kriesel extends to 2023-03-23, and has NOT been ceded. (reserved anyway on the https://www.mersenne.ca/obd page by Rafael R for P-1 ~2023-03-02)

29 other exponents have been completed to 90 bits, and are available for reservation to a higher TF level.
These are in the exponent range up to 3321929987, as part of an effort to go to ~30 exponents eventually remaining with no known factors after TF and P-1 factoring completion to recommended levels and bounds, for eventual PRP/GEC/proof & CERT when hardware and software development advance sufficiently. Anyone with a sufficiently fast GPU, or fast CPU with at least 64 GiB ram, is welcome to help with TF or P-1 respectively. (But please follow the rules!)

At the moment:
OBD TF completed to 92 bits, reserved for P-1 and in progress in P-1 stage 2: 3
OBD TF completed to 92 bits, by Kriesel 2023-02-23, so restricted for reservation to kriesel until 2023-03-23: 1
OBD TF completed to 92 bits, ready for reservation by anyone with qualified hardware for P-1: 0
OBD TF completed to 91 bits: 0
OBD TF completed to 90 bits, reserved to 91 bits: 0

Systems with qualification(s) completed & posted for OBD P-1: 3 (1 is unconditionally)
Exponents completed thru stage 1 P-1: 3
Exponents completed thru stage 2 P-1: 0
kriesel is the only user that has yet posted system qualification results.

(This status summary is specific to OBD Mersennes. See also Ernst Mayer's F33 P-1 effort, mentioned in the Xeon Phi hardware thread.)

[kriesel]

OBD P-1 is now feasible. For now, Mlucas v20.x is the only known software capable of OBD Mersenne P-1 factoring, with sufficiently large fft lengths and several months of QA testing and revision (patching) accomplished. The latest version is recommended, which is V20.1.1 patch 2022-07-06. See http://www.mersenneforum.org/mayer/README.html and https://mersenneforum.org/showthread.php?t=27295

I propose the following:

1. OBD candidates are taken to 92 bits TF done, before P-1 is attempted. (Due to run time, RTX206x or faster GPUs and mfaktx are recommended. TF reservations that would take longer than a year on available hardware ought be avoided.)
2. P-1 is only attempted on OBD candidates with no known factors, except for software testing in which finding again a known factor supports confidence in the P-1 software on the tested FFT length.
3. Whoever does the TF from 91 bits to 92 (which is half the total work of trial factoring an exponent up to 92 bits) gets first choice at reserving the P-1 for the same exponent, for the month following 92-bit completion. The individual may be operating under different usernames in the Mersenne forum and on mersenne.ca. Announcement in the OBD subforum of intent to complete a specific exponent's TF to 92 bits, followed by initiation and completion of that exponent to 92 bits under a different mersenne.ca user name shall constitute sufficient proof that the two user names correspond to the same individual. That individual may retain priority on P-1 on the exponent by making a clear reservation on https://www.mersenne.ca/obd (or previously, in this thread), or cede the option to another specific individual or group, by posting clearly his intent in this thread including the recipient(s), or surrender the option entirely. (Something analogous to "I cede the option to reserve exponent 332192xxxx P-1 to user(s) insert-forum-name(s)-here".) Prior agreement by PM that the recipient(s) will commit to timely reserving and completing the P-1 is recommended in the case of ceding the option, as is prior qualification of hardware by the recipient(s). The option period does not reset upon ceding. Ceding recursively is discouraged. If the TF-to-92 user decides not to attempt P-1 on the exponent, announcing that in this thread promptly would be helpful.
4. In the absence of a reservation by the TF-to-92-bits user (or if the option is ceded to others, by those others) and after a month past TF completion to 92 bits, or upon the TF-to-92 user posting its release before a month passes, the exponent becomes fair game for anyone with sufficient (qualified) hardware resources to reserve for P-1.
5. P-1 is estimated to be ~21,663. GHzDays per attempt of both stages without factor found early, 5,220. GHzDays per attempt of stage 1 only, and require ~16 GiB of ECC ram in stage 1, ~64 GiB of ECC ram per system in stage 2. (128 GiB of ECC ram per system would be better in stage 2.) Those who haven't the hardware resources to complete that within a year ought not make solo P-1 reservations or attempts. (~59.4 GHzD/day minimum at ~192M fft length needed for completion of both stages solo within one year running continuously nonstop. Roughly a Xeon Phi 7210 or dual-12-core Xeon e5-2697v2)
6. To qualify for reserving OBD exponents for P-1, post in this thread, results of run-time scaling derived from multiple widely-spaced exponents full P-1 runs, including near the first test wavefront, above 100Mdigit, and ideally also nearer 1Gbit, that demonstrates scaling consistent with completion within a year for OBD P-1, on the hardware planned to be used, along with a description of the software and hardware, sufficient for OBD P-1. Some run time scaling examples are posted at the Mlucas v20.1.x P-1 run time scaling reference post. Post title beginning with "Qualification" is suggested. To increase total possible throughput and participation, qualification either unconditionally, capable of completion of both stages within one year on one system, or conditionally, capable of completion within one year for a single stage or by splitting stage 2 with another equal or faster system, are allowed. Conditional qualifications should include " (conditional)" in the post title. Allow plenty of time for performing qualification, which may take weeks or months. Users intending to qualify multiple systems are encouraged to include a system name in each qualification post. Stating OS, Mlucas version, CPU model, available ram and type, and estimated OBD P-1 completion time are required.
7. Optionally, systems tested and found to fail qualification may be posted, possibly saving others the time and effort of futile attempts to qualify similar hardware. At least the CPU model should be stated, and additional details required for qualification are encouraged. Post title should begin with "Disqualification".
8. Reservation for OBD P-1 or TF is performed at https://www.mersenne.ca/obd. Previously, P-1 reservation was, and for joint P-1 efforts still should include, posting a statement in this thread, of intent to P-1 factor a specific exponent. Post title "Reservation " followed by the exponent and whether the reservation is joint, solo, for both stages or only stage 1, is suggested. For example, "Reservation 3321928307 solo both P-1 stages", "Reservation 3321928171 joint both P-1 stages", "Reservation 3321928319 solo P-1 stage 1", "Reservation 3321928319 joint P-1 stage 2". Stage 2 is possible to do as a split effort with multiple systems, or joint effort with systems by multiple users; stage 1 is not. "Joint P-1 stage 1" is an oxymoron and constitutes an invalid reservation that will be ignored. Explicitly stating P-1 is proposed, to preclude possible uncertainty if P+1 or other multistage factoring becomes available for OBD exponents in the future.
9. Joint reservations should be posted in this thread by the user who completed the TF to 92 bits (or by whomever he ceded the right to), if posting in the one-month option period. Otherwise reservation posting may be done by whoever is selected by mutual agreement in PM among the joint effort participants. All participants in a joint effort should be identified in the joint reservation post.
10. P-1 reservations omitting joint, solo, or stage, from subject and body, will be presumed solo for both stages. Full specification is encouraged.
11. P-1 reservations omitting identification of joint effort participants other than the poster may be treated as a single-user effort. Coordination and ensuring completion and result reporting in a joint effort is nominally the responsibility of the poster of the reservation.
12. Use P-1 bounds corresponding to the target row for the exponent at mersenne.ca. https://www.mersenne.ca/exponent/3321928307 shows B1=17,000,000, B2=1,000,000,000.
13. Updating TF and P-1 assignment progress and ETA frequently at https://www.mersenne.ca/obd are strongly recommended. Reporting P-1 progress in this thread roughly monthly to quarterly is requested. (4-12 times per year.) Include exponent, stage, % complete, ETA. For joint efforts, update stage 2 progress by participant and system also. Dialogue by PM among joint participants for a specific reservation is recommended to establish participation, settle details such as stage 2 bounds split, etc (rather than chatty posting in this thread)
14. Reservations expire after any of the following occur:
    1. One year passes after the last progress report that showed progress on that reservation.
    2. Two years pass after initial reservation.
    3. A factor is found and reported here.
    4. The user posts surrender of a reservation here.
    5. The factoring attempt is completed without finding a factor and is reported here. (In a joint attempt, that would require completion and reporting of all the reservation's participants' portions of the split stage 2.)
15. If a new factor is found, or a reservation completed without finding a factor, it should be reported as a single line input in https://www.mersenne.ca/obd. Or put the result(s) in a text file and upload at https://www.mersenne.ca/bulk-factors.php
16. Reservation and other status for exponents 3321928171 through 3321929987 will be maintained in a Libre Office spreadsheet by kriesel, and periodic snapshots posted in this thread.
17. Revision of reservations are to be avoided, but may be performed by posting clearly in this thread, for justifiable reasons such as time deadlines, equipment failure, etc, and must include the exponent and change. It might involve converting a solo reservation to joint, or shortening from both stages to stage 1. Revisions ought meet the same information content requirements as initial reservation.
18. For reservations for only stage 1, the user should plan on preserving the stage 1 files until such time as a user reserves stage 2 on the same exponent, or a central repository for such files is established, and make all reasonable and necessary effort to transfer the stage 1 files for reuse, and ensure their correctness.

Constructive civil comments are invited.

[kriesel]

Originally Posted by kriesel

(run to mersenne.ca lookup gpu72 row bounds)

Since the mersenne.ca pages have been changed, this is now called the target row.

Originally Posted by kriesel

(reserved anyway on the https://www.mersenne.ca/obd page by Rafael R for P-1 ~2023-03-02)

Shortly after being made aware of this thread (IIUC by James Heinrich), Rafael R graciously unreserved M3321928373.
A proper P-1 on it requires ~21663. GHD, which would have been comparable effort to 3/4 of the total mersenne.org P-1 GHD credits for him in the preceding year. (Which I think were produced mostly by the more efficient new stage 2 code of mprime, while OBD P-1 requires Mlucas for sufficiently large fft length.) OBD work produces no GHD credits on mersenne.org, whether performing TF or P-1.

Exponent status update attached below.

[alpertron]

Originally Posted by kriesel

Use P-1 bounds corresponding to the GPU72 row for the exponent at mersenne.ca. https://www.mersenne.ca/exponent/3321928307 shows B1=17,000,000, B2=1,000,000,000.

I suggest to perform a preliminary P-1 with B1 = 1M, B2 =50M. If no factor is found, use the bounds you suggest above.

[kriesel]

Originally Posted by alpertron

I suggest to perform a preliminary P-1 with B1 = 1M, B2 =50M.

Why? Odds of a factor at the full indicated bounds after TF to 92 bits are only 3.98%: https://www.mersenne.ca/prob.php?exp...&b2=1000000000
Please, before your response, see https://www.mersenneforum.org/showpo...9&postcount=20, and R.D. Silverman's comments on the matter and the rest of that thread, and consider that for OBD P-1, Mlucas v20.x will be required, which does periodic GCDs during stage 2, lowering stage 2 cost in the case of a stage 2 factor found. (Which I think improves further the case for full bounds from the start, compared to only a single GCD after completing stage 2.) We expect to do dozens of OBD P-1 in the course of taking OBD to "level 28" or higher, by relatively few very determined participants, so what is statistically expected to be most efficient in the long run is relevant.

(Footnotes:
currently, there is no PrimeNet row or GPU72 row, only "target" row, which corresponds to the older GPU72;
ECM as as a followup to prior P-1 as suggested in https://mersenneforum.org/showpost.p...0&postcount=31 is not an option, since there is no implementation for OBD exponents.)

[alpertron]

Originally Posted by kriesel

Why? Odds of a factor at the full indicated bounds after TF to 92 bits are only 3.98%: https://www.mersenne.ca/prob.php?exp...&b2=1000000000
Please, before your response, see https://www.mersenneforum.org/showpo...9&postcount=20, and R.D. Silverman's comments on the matter and the rest of that thread, and consider that for OBD P-1, Mlucas v20.x will be required, which does periodic GCDs during stage 2, lowering stage 2 cost in the case of a stage 2 factor found. (Which I think improves further the case for full bounds from the start, compared to only a single GCD after completing stage 2.) We expect to do dozens of OBD P-1 in the course of taking OBD to "level 28" or higher, by relatively few very determined participants, so what is statistically expected to be most efficient in the long run is relevant.

The probability of finding a factor with B1 = 1M, B2 = 50M is 1.54% while being about 20 times faster than B1 = 17M, B2 = 1000M.

So about 39% of the positive results you will find with P-1 in OBD would have been found a lot faster by using lower bounds. For the other 61%, there is almost no difference on running both instances of P-1.

[kriesel]

So for the average case, and taking your 20:1 as a given without question, we have for your proposal, since for 1.54% of the exponents we run only the short small bounds and find a factor, while for the other 98.46% of exponents, we run both a small-bounds set and a full-bounds set, giving (ignoring the small chances of finding a factor in full bounds stage 1 that eluded the small bounds both stages, or finding a factor in small-bounds stage 1 that eluded trial factoring) a cost for P-1 effort of roughly
.0154 * .05 + 0.9846 * (0.05 + 1) = 1.0346,
instead of 1. * 1 = 1 for running full bounds the first time every time, giving on average, an estimate that low-bounds first costs a few percent MORE P-1 effort than full bounds initially.
Mlucas IIRC does not have B1 extension later from a saved file. Mlucas does periodic GCD during stage 2, so we may as well aim for the full B2, and if we get lucky and it finishes early with a factor found, great, some cycles saved.

To prepare for levels 29 and 30 (PRP, and proof or DC, respectively), we'll TF ~33-34 exponents to 92 bits, finding factors for 1-2 of them; then P-1 to full bounds ~31-32, to have 30 PRP candidates surviving the full complement of optimal-compute-effort-level factoring attempts. https://www.mersenne.ca/obd shows 33 at 90 bits TF or higher now. (1.0346-1) * 32 ~ 1.107 extra P-1 effort from doing small-bounds P-1 first.
.0154*32 = 0.4928, so it's ~50-50 we find NO factors with small-bounds P-1.

[alpertron]

Yes, you are right. It is better not use small P-1, especially if the software performs GCD in the middle of a step.

Another way it helps using small p-1 is if there are memory errors during a very long run. It is possible that doing P-1 with large bounds skips the factors that could have been found by P-1 with smaller bounds because (in our case) 95% of the errors would be introduced by the long P-1 run.

[kriesel]

Hence, why ECC ram, time limits on run lengths, and qualifying run-time scaling with re-finding known factors are proposed. And better software error detection may be added to P-1 in various software titles later;
see https://www.mersenneforum.org/showpo...37&postcount=3 and
from the Announcements page,
"There's a paper describing a generalization of GEC and VDF, which appears to allow adding the same excellent error detection and verification now available for PRP, to P-1 stage 1 computations. Discussion starts here in https://mersenneforum.org/showthread.php?t=24654."