M1781699 Mersenne number exponent details

is 2 ^1781699 - 1

has 536345 decimal digits

takes 0.097 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	16.6773	68.6567%	500000	15000000	0.1015	5.0523%	16.7788	70.2403%	1.5835%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8120%	0.0120	64.1939%	1.0360%
GPU72	2⁶¹	0.1724	65.5738%	8000	130000	0.0012	1.4919%	0.1736	66.0874%	0.5136%
Difference	+6	+16.5049	+3.0829%	+492000	+14870000	+0.1003	+3.5603%	+16.6052	+4.1529%	+4.1529%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1781699	213803881	9	27.672	60 2² × 3 × 5	-	4	5	1.017e-11	3.189e-7	6.404e-7
1781699	1286386679	10	30.261	361 19²	2008-07-15	361	361	8.656e-11	2.840e-5	5.779e-5
1781699	62528615939663	14	45.830	17547469 19 × 923551	2014-01-30	19	923551	3.034e-6	0.0040	0.0074
1781699	240790233549702155279	21	67.706	67573207806061 67573207806061	2018-12-01	1	67573207806061	31.061	289,602	540,896
1781699	16632424275424620387377	23	73.816	4667574117576712 2³ × 583446764697089	2020-05-19	8	583446764697089	2,047.8	2,500,507	4,670,251

exponent	prime factors	composite factor	digits	bits*
1781699	213803881 1286386679	275034464436901199	18	57.932
1781699	213803881 62528615939663	13368860761458411232103	23	73.501
1781699	1286386679 62528615939663	80435978601089550949177	23	76.090
1781699	213803881 240790233549702155279	51481886439822727192714837799	29	95.378
1781699	1286386679 240790233549702155279	309749348871635736968495128441	30	97.967
1781699	213803881 16632424275424620387377	3556076860524396761772926010137	31	101.488
1781699	213803881 1286386679 62528615939663	17197524396945896821481276355937	32	103.762
1781699	1286386679 16632424275424620387377	21395729027382458734953592550983	32	104.077
1781699	62528615939663 240790233549702155279	15056280035651082660124584920930977	35	113.536
1781699	62528615939663 16632424275424620387377	1040002469663553741641772359918833951	37	119.646
1781699	213803881 1286386679 240790233549702155279	66225612925978691382159433190279279521	38	125.639
1781699	213803881 1286386679 16632424275424620387377	4574489902878724948855428442292855765023	40	131.749
1781699	213803881 62528615939663 240790233549702155279	3219091105045019834586440199609121015721737	43	141.208
1781699	240790233549702155279 16632424275424620387377	4004925325777229988728731828682540785513183	43	141.523
1781699	1286386679 62528615939663 240790233549702155279	19368198073155197825912150522689877091255383	44	143.797
1781699	213803881 62528615939663 16632424275424620387377	222356564263652554215082242269175543718363831	45	147.318
1781699	1286386679 62528615939663 16632424275424620387377	1337845323102297145048583553749981515779338729	46	149.907
1781699	213803881 240790233549702155279 16632424275424620387377	85626857776636111301978912118055433688350710206322 3	51	169.194
1781699	213803881 1286386679 62528615939663 240790233549702155279	41409959160173032105027801468072742815233920475414 23	52	171.468
1781699	1286386679 240790233549702155279 16632424275424620387377	51518825894695639790199607689805305863583547900892 57	52	171.783
1781699	213803881 1286386679 62528615939663 16632424275424620387377	28603652225697008962660709734451815175188535987380 7249	54	177.578
1781699	62528615939663 240790233549702155279 16632424275424620387377	25042243756255413612748247485274288633447371936921 9077329	57	187.352
1781699	213803881 1286386679 240790233549702155279 16632424275424620387377	11014924920849225100922701888757818528026219108960 23483006417	61	199.455
1781699	213803881 62528615939663 240790233549702155279 16632424275424620387377	53541289040354254576658063883001332593452345293643 910672179313849	65	215.024
1781699	1286386679 62528615939663 240790233549702155279 16632424275424620387377	32214008780317886993074610145652093559267813107214 7703708696500391	66	217.613
1781699	213803881 1286386679 62528615939663 240790233549702155279 16632424275424620387377	68874800998000406528387717717023928787465619607051 870058157405234713817471	74	245.285

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:33:24	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 213803881 skipped known factor: 1286386679 skipped known factor: 62528615939663	-	-	0.101	-	-	5.052%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	1286386679	30.261	10	6.27328e-12	0.207	1.34441e-11
2014-01-30T08:34:00	TJAOI	Manual testing	?	?	62528615939663	45.830	14	4.03723e-7	0.207	8.65184e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.767 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	17.767 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.323	0.024%
25	50000	0.752	47.133%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		253	17.42
50000	5000000	240790233549702155279	3	0.207
50000	5000000	16632424275424620387377	2	0.138

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-12T23:29:19	alpertron	laptop2	50000	5000000						3	0.207
2018-12-01T12:12:34	Chang Chia-Tche	exbpc13	50000	5000000	240790233549702155279	67.706	3	2		3	0.207
2020-03-08T07:29:55	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-03-21T07:18:41	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-29T09:21:42	Greg	azure	50000	5000000						3	0.207
2020-05-19T22:02:33	nordi	sweet16	50000	5000000	16632424275424620387377	73.816	2	2	1233344114661468	2	0.138
2020-06-13T01:06:25	nordi	sweet16	50000	5000000						3	0.207
2020-07-07T01:12:30	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-08-09T16:37:49	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-10-13T22:44:54	nordi	sweet16	50000	5000000						7	0.482
2020-10-30T10:29:41	TJAOI	Manual testing	50000	5000000						225	15.49

Lucas-Lehmer results:
No L-L results for M1781699

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T14:20:43

Oliver Kruse

GTX-3

213803881

1286386679

62528615939663

0C817B47B46690__

2017-11-04T19:27:01

ATH

ec2-1xf

213803881

1286386679

62528615939663

0C817B47B46690__

2018-12-01T12:20:02

rucio

213803881

1286386679

62528615939663

240790233549702155279

721567AD24C1BF__

2018-12-03T09:53:22

Oliver Kruse

GTX-4

213803881

1286386679

62528615939663

240790233549702155279

721567AD24C1BF__

2020-05-20T00:34:09

CrypticClue

cruncher

213803881

1286386679

62528615939663

240790233549702155279

16632424275424620387377

721567AD24C1BF67

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-10-30T10:29:41+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront