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Old 2020-05-25, 03:19   #12
kriesel
 
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"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

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Default Interim residues for Mersenne number large exponents

For purposes of this post, "large exponents" means well ahead of the first test wavefront, which is at ~102M-114M as of March 2021.
Note, while both PRP and LL interim residues are listed here, PRP with GEC and proof generation should be used for large exponents and first-test wavefront exponents whenever practical. High proof powers, at least 8 are recommended. Proof generation enables verification at ~1% or less the effort of a traditional full double check. GEC essentially eliminates error in final residue results. At 100Mdigit, a small sample of results of LL & DC & TC indicates an error rate of about 20% per test. That is consistent with error proportional to run time. Extrapolating to higher exponent indicates high probability of error near 1G. (Run time of 999M is (999/332)2.1= 10.1 times longer; 1 - (1-0.20)10.1 = 0.89, 89% probability of bad result.)


~50Mdigit interim residues
166000013 from a complete PRP3 with proof certified valid (49,970,984 decimal digits) FFT: 9M 1K:9:512 (17.59 bpw)
gpuowl-win-v6.11-364-g36f4e2a
2020-08-09 04:21:37 asr2/radeonvii0 166000013 OK 800 0.00%; 1418 us/it; ETA 2d 17:23; 9c30f47224fb8783 (check 0.96s)
2020-08-09 04:26:20 asr2/radeonvii0 166000013 OK 200000 0.12%; 1417 us/it; ETA 2d 17:15; c6ae0c584288f318 (check 0.94s)
2020-08-09 04:45:17 asr2/radeonvii0 166000013 OK 1000000 0.60%; 1417 us/it; ETA 2d 16:56; 8d41ce621b768b00 (check 1.03s)
2020-08-09 08:18:39 asr2/radeonvii0 166000013 OK 10000000 6.02%; 1416 us/it; ETA 2d 13:22; b8fba9175797f5ed (check 0.95s)
2020-08-11 07:15:04 asr2/radeonvii0 166000013 OK 100000000 60.24%; 1418 us/it; ETA 1d 02:00; b00fa62adb2d712c (check 0.95s)


100Mdigit interim residues
mlucas v17.0 LL 1 core of a xeon e5645 (Not recommended; at these timings, actually msec not sec/iteration, a full run is over 8 years; v17.0 did not include the Jacobi check. The odds of correct completion over such a long run are negligible.)
332220523 100,008,343 decimal digits
[Jul 22 13:31:39] M332 220 523 Iter# = 10000 [ 0.00% complete] clocks = 02:16:04.515 [816.4516 sec/iter] Res64: 1A313D709BFA6663. AvgMaxErr = 0.171224865. MaxErr = 0.250000000.
[Jul 23 09:51:21] M332220523 Iter# = 100000 [ 0.03% complete] clocks = 02:16:05.131 [816.5132 sec/iter] Res64: 91B688264B5B3F39. AvgMaxErr = 0.171926060. MaxErr = 0.250000000.
[Jul 31 21:47:38] M332220523 Iter# = 1000000 [ 0.30% complete] clocks = 02:15:44.087 [814.4088 sec/iter] Res64: 7CC62737AA46CDF8. AvgMaxErr = 0.171821204. MaxErr = 0.234375000.
[Oct 26 19:22:44] M332220523 Iter# = 10000000 [ 3.01% complete] clocks = 02:20:19.131 [841.9132 sec/iter] Res64: 2B8CC43403D28DAC. AvgMaxErr = 0.171851920. MaxErr = 0.250000000.

DoubleCheck=332220523
gpuowl v6.11-292 (manageable projected total time at 15 days on a Radeon VII)
2020-05-24 20:41:20 asr2/radeonvii3-w2 332220523 LL 100000 0.03%; 3843 us/it; ETA 14d 18:33; 91b688264b5b3f39
2020-05-24 21:39:36 asr2/radeonvii3-w2 332220523 LL 1000000 0.30%; 3870 us/it; ETA 14d 20:03; 7cc62737aa46cdf8
(version?)
2020-07-30 09:48:45 asr2/radeonvii2 332220523 LL 2000000 0.60%; 3722 us/it; ETA 14d 05:25; 627dfa42f70bd3b4
(LL residues above for M332220523 are otherwise unverified; passed Jacobi checks where applicable)

gpuowl v6.0-b7bb1c3 PRP 332220523 on an RX480
2019-02-04 23:30:02 condorella/rx-480 332220523 OK 10000 0.00%; 16.52 ms/sq; ETA 63d 12:29; 503cd91d7b8e30e5 (check 7.48s)
continuation on gpuowl v6.10-9-g54cba1d
2021-03-15 18:04:59 332220523 100000 0.03%; 18714 us/sq; ETA 71d 22:30; 951c94f813216db9
continuation on gpuowl v6.11-380-g79ea0cc
2021-03-15 18:33:02 condorella/rx480 332220523 OK 200000 0.06%; 14796 us/it; ETA 56d 20:39; 6cd7d19bb77ad049 (check 6.58s)
2021-03-15 19:22:27 condorella/rx480 332220523 OK 400000 0.12%; 14793 us/it; ETA 56d 19:30; b12cf8adffda122c (check 6.56s)

gpuowl (version?) independent run on a 5700xt:
2020-09-03 13:13:03 asr2/5700xt 332220523 OK 200000 0.06%; 7520 us/it; ETA 28d 21:34; 6cd7d19bb77ad049 (check 4.05s)


~gigabit or 300Mdigit interim residues (mostly unverified, except for green)
CUDALucas v2.06 on gtx1080ti (LL, no Jacobi check, unverified; not recommended at 1.4 years estimated duration on a GTX1080Ti)
999999937 301,029,977 decimal digits
| Jan 09 04:48:51 | M999999937 10000 0x567ad47461d3bb5f | 57344K 0.21875 41.1682 41.16s | 473:21:41:27 0.00% |
| Jan 20 08:14:38 | M999999937 100000 0xe776f4a0dcd3491d | 57344K 0.18750 44.3713 44.37s | 506:19:41:57 0.01% |
| Jan 20 19:26:39 | M999999937 1000000 0x141a108c13a86d5a | 57344K 0.18750 45.3946 45.39s | 516:19:59:55 0.10% |
| Jan 23 07:03:54 | M999999937 5000000 0x0811f10855dab84c | 57344K 0.20313 44.9825 44.98s | 516:10:56:38 0.50% |


gpuowl v6.11-380-g79ea0cc independent run from start on gtx 1080
2021-03-27 14:28:07 gpuowl v6.11-380-g79ea0cc
2021-03-27 14:29:16 asr3/gtx1080 999999937 LL 1000 0.00%; 52191 us/it; ETA 604d 01:29; ddadfed64e080856
(Jacobi check on exit passed; continuing:)
2021-03-27 14:55:18 asr3/gtx1080 999999937 LL 10000 0.00%; 50442 us/it; ETA 583d 19:32; 567ad47461d3bb5f
2021-03-27 15:03:46 asr3/gtx1080 999999937 LL 20000 0.00%; 50782 us/it; ETA 587d 17:50; 78a2f270a1bba92d
2021-03-27 15:12:14 asr3/gtx1080 999999937 LL 30000 0.00%; 50794 us/it; ETA 587d 21:05; d79b942904525426
2021-03-27 15:20:42 asr3/gtx1080 999999937 LL 40000 0.00%; 50823 us/it; ETA 588d 05:02; 650ca8c106ac7d12
2021-03-27 15:29:11 asr3/gtx1080 999999937 LL 50000 0.01%; 50869 us/it; ETA 588d 17:34; 98420630c9a4b877
2021-03-27 15:37:39 asr3/gtx1080 999999937 LL 60000 0.01%; 50850 us/it; ETA 588d 12:03; adb31fa7cf23b0ba
2021-03-27 15:46:08 asr3/gtx1080 999999937 LL 70000 0.01%; 50847 us/it; ETA 588d 11:13; 20b88580b0d5c8a5
2021-03-27 15:54:38 asr3/gtx1080 999999937 LL 80000 0.01%; 51002 us/it; ETA 590d 06:05; 2b4ab3e44fcbdc84
2021-03-27 16:03:07 asr3/gtx1080 999999937 LL 90000 0.01%; 50957 us/it; ETA 589d 17:20; b9c6eeca4e553904
2021-03-27 16:11:37 asr3/gtx1080 999999937 LL 100000 0.01%; 50972 us/it; ETA 589d 21:24; e776f4a0dcd3491d

CUDALucas V2.06beta on V100 (LL, no Jacobi check, unverified, ~6 months; interim residue extracted by ramgeis from an interim save file using a perl program provided by Kriesel)
999999937 Iteration 110,000,000 Residue64 0x87ded9d3ab3e7f38
See also https://mersenneforum.org/showthread...859#post495859


The PRP equivalent is feasible marginally with Gpuowl on a Radeon VII, at ~0.51 years to complete; LL in Gpuowl on a Radeon VII is also possible but not recommended since it's only protected by an occasional Jacobi check's ~50% chance of detection of an error. Such long runs are likely to go wrong with undetected errors.
Gpuowl v6.2-e2ffe65 PRP on RX480:
2019-02-08 17:48:10 condorella/rx480 999999937 10000 0.00%; 72.02 ms/sq; ETA 833d 14:01; a30a0c45e9fb828c
2019-02-08 21:16:26 condorella/rx480 999999937 100000 0.01%; 74.38 ms/sq; ETA 860d 18:51; 3efc806b68d92b86
continuation on gpuowl v6.11-380-g79ea0cc on RX480, quite a speed improvement, 1.51X over v6.2, but still not recommended at ~1.56 years on an RX480:
2021-03-16 12:20:54 condorella/rx480 999999937 OK 1000000 0.10%; 49236 us/it; ETA 569d 07:00; e1b53ccf581f928b (check 22.08s)


1.5Gbit interim residues
gpuowl v4.6 PRP on RX480 (not recommended, at estimated 7.8 years to completion; also moot since it has a known small factor) Following is combined PRP/P-1, type 0, B1 bounds 0, so presumably base = 3.
2018-11-01 16:35:37 condorella-rx480 10000/1500000041 [ 0.00%], 164.51 ms/it [163.50, 174.58]; ETA 2856d 01:42; 4fc4ebb3728095f7
CUDALucas 2.06 fails on 1,500,000,043 with an error similar to that for 2Gbit (see below).


2Gbit interim residues
P-1 stage 1 appears possible on gpuowl v6.11-380, at over 6 days on a Radeon VII:
2021-03-26 13:57:40 asr2/radeonvii4 2147483563 P1 B1=11000000, B2=600000000; 15869712 bits; starting at 0
2021-03-26 14:02:48 asr2/radeonvii4 saved
2021-03-26 14:03:21 asr2/radeonvii4 2147483563 P1 10000 0.06%; 34113 us/it; ETA 6d 06:17; d78cbf554970d8c1

https://www.mersenne.ca/exponent/2147483743 Projected PRP time on a Radeon VII is 2.63 years, not recommended. Gpuowl V6.11-380 PRP interim residues with timings:
2021-03-26 12:43:44 asr2/radeonvii4 2147483743 OK 20000 0.00%; 38636 us/it; ETA 960d 07:01; 304a08968e896b20 (check 23.14s)
2021-03-26 13:36:46 asr2/radeonvii4 2147483743 OK 100000 0.00%; 38636 us/it; ETA 960d 05:56; 0637bf5d33611a9d (check 22.85s)


gigadigit ~3.3gigabit interim residues
Gpuowl v6.5-84 PRP3 (not recommended at an estimated 6.3 years on a Radeon VII; lacks PRP proof capability)
M3,321,928,097 1,000,000,001 decimal digits (This one is moot as it has multiple known small factors)
FFT 196608K: Width 512x8, Height 256x8, Middle 12; 16.50 bits/word
2020-05-24 17:21:43 radeonvii3 3,321,928,097 20000 0.00%; 60053 us/sq; ETA 2308d 21:54; 1a05f0ca51fb8e7a
2020-05-24 18:41:56 radeonvii3 3,321,928,097 100000 0.00%; 60122 us/sq; ETA 2311d 12:24; 5b2cb77f57840bcc


Top of this thread https://www.mersenneforum.org/showthread.php?t=24003
Top of reference tree: https://www.mersenneforum.org/showpo...22&postcount=1

Last fiddled with by kriesel on 2021-03-28 at 18:59 Reason: more interim residues added; high error rate caution on LL on large exponents
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