M203657 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	145.9018	73.1343%	30000000	10264076402580	3,739.1646	23.1721%	3,885.0664	79.3597%	6.2253%
PrimeNet	2⁴⁰	0.0000	55.0000%	2200	50000	0.0000	12.6794%	0.0000	60.7057%	5.7057%
GPU72	2⁴⁴	0.0000	59.0909%	3600	80000	0.0001	8.8921%	0.0001	62.7286%	3.6377%
Difference	+23	+145.9018	+14.0434%	+29996400	+10264076322580	+3,739.1645	+14.2800%	+3,885.0663	+16.6311%	+16.6311%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
203657	6109711	7	22.543	15 3 × 5	-	3	5	2.753e-12	2.079e-8	4.082e-8
203657	158455369581401	15	47.171	389025100 2² × 5² × 113 × 173 × 199	2014-02-27	173	199	0.0001	1.166e-6	2.354e-6
203657	448821536522329129	18	58.639	1101905499252 2² × 3 × 107 × 257 × 3339229	2014-07-28	257	3339229	0.3433	0.0012	0.0023
203657	135135144122148732391	21	66.873	331771419892635 3 × 5 × 2626873 × 8419933	2014-07-28	2626873	8419933	128.03	0.0197	0.0357
203657	132602900510114310940573183	27	86.777	325554487471862766663 3 × 7 × 13² × 91731329239747187	2020-05-31	169	91731329239747187	112,977,059	33,415,685	62,411,194
203657	7639839012609820796998312583	28	92.626	18756632506149606438763 23 × 802516307 × 1016185906783	2019-11-20	802516307	1016185906783	9.448e+9	375.25	691.38

exponent	prime factors	composite factor	digits	bits*
203657	6109711 158455369581401	968116514540551085111	21	69.714
203657	6109711 448821536522329129	2742169878727376025071719	25	81.182
203657	6109711 135135144122148732391	825636676529677453925349001	27	89.416
203657	158455369581401 448821536522329129	71118182445737929030762278929729	32	105.810
203657	6109711 132602900510114310940573183	810165399878551016811040322480113	33	109.320
203657	158455369581401 135135144122148732391	21412889205310966391659552439859791	35	114.044
203657	6109711 7639839012609820796998312583	46677208453571360831449357369793513	35	115.168
203657	448821536522329129 135135144122148732391	60651563023069187818792989574245117439	38	125.512
203657	6109711 158455369581401 448821536522329129	434511541588731928116467633962033498319	39	128.353
203657	158455369581401 132602900510114310940573183	21011641607895910331750231278929716169383	41	133.948
203657	6109711 158455369581401 135135144122148732391	130826564719469669783752675796888203530401	42	136.587
203657	158455369581401 7639839012609820796998312583	1210573514285494849182604133912224061068783	43	139.797
203657	448821536522329129 132602900510114310940573183	59515037554267046098251324438493849437147607	44	145.416
203657	6109711 448821536522329129 135135144122148732391	370563521769239070577545535124650710713350129	45	148.055
203657	448821536522329129 7639839012609820796998312583	3428924284422773595950234556652401913948130207	46	151.265
203657	135135144122148732391 132602900510114310940573183	17919312071449247074095482883142789234418070553	47	153.650
203657	6109711 158455369581401 132602900510114310940573183	128375057859819330208908037297420955106957178313	48	156.491
203657	135135144122148732391 7639839012609820796998312583	1032410746039042600278160413691730171779434975953	49	159.499
203657	6109711 158455369581401 7639839012609820796998312583	7396254316538745020494297485608988380376615251713	49	162.339
203657	6109711 448821536522329129 132602900510114310940573183	36361967961071846848399319768643469533848454311157 7	51	167.959
203657	158455369581401 448821536522329129 135135144122148732391	96105658345100630615325971646342259117007655151520 39	52	172.683
203657	6109711 448821536522329129 7639839012609820796998312583	20949736418704948489686703523359303150069944555140 177	53	173.807
203657	6109711 135135144122148732391 132602900510114310940573183	10948181807536625079031898682144921395620566425644 0183	54	176.193
203657	132602900510114310940573183 7639839012609820796998312583	10130648125023900197766552763947312785336624418212 61689	55	179.403
203657	6109711 135135144122148732391 7639839012609820796998312583	63077312915929450043880797392969144395527034463647 79583	55	182.041
203657	158455369581401 448821536522329129 132602900510114310940573183	94304772713123446631268387372096789966584289312590 38857407	58	192.587
203657	6109711 158455369581401 448821536522329129 135135144122148732391	58717779795330311897739385755334541029203195776345 079350729	59	195.226
203657	158455369581401 448821536522329129 7639839012609820796998312583	54333146475485155003743631376997007148322034398158 8233480007	60	198.436
203657	158455369581401 135135144122148732391 132602900510114310940573183	28394112169259507675506337796077623915710436734235 49694584753	61	200.821
203657	6109711 132602900510114310940573183 7639839012609820796998312583	61895332286587898301196482853969300345011812910822 22575161879	61	201.946
203657	158455369581401 135135144122148732391 7639839012609820796998312583	16359102632342642379164081783703849929852936932887 4016111050153	63	206.670
203657	448821536522329129 135135144122148732391 132602900510114310940573183	80425731773309714843983114301919472087021643751979 97021809038337	64	212.289
203657	6109711 158455369581401 448821536522329129 132602900510114310940573183	57617490719787016624097341027956085072352966484031 593556526979377	65	215.130
203657	448821536522329129 135135144122148732391 7639839012609820796998312583	46336817735940722157509130552470445280147095424792 1174909666434937	66	218.137
203657	6109711 158455369581401 448821536522329129 7639839012609820796998312583	33195982268588288186307750580398376154118176510480 93427563367047977	67	220.978
203657	6109711 158455369581401 135135144122148732391 132602900510114310940573183	17347981945575867589962550260241121569167912812996 269228051105836383	68	223.364
203657	158455369581401 132602900510114310940573183 7639839012609820796998312583	16052555927497891901932926929509128874706642121097 8930313381608246289	69	226.574
203657	6109711 158455369581401 135135144122148732391 7639839012609820796998312583	99949389302952797913044961278795032658771717161168 4193847860341335783	69	229.212
203657	6109711 448821536522329129 135135144122148732391 132602900510114310940573183	49137797809843987118914691726469471972426909406955 329582113921426990607	71	234.832
203657	448821536522329129 132602900510114310940573183 7639839012609820796998312583	45468530574402795348215048754222095979123645374927 3609131447095696438881	72	238.042
203657	6109711 448821536522329129 135135144122148732391 7639839012609820796998312583	28310456502627212551367726753686475670301279053490 20729478513023865373207	73	240.680
203657	135135144122148732391 132602900510114310940573183 7639839012609820796998312583	13690065944258805834377418818756967511134875314687 3437095851116703641668399	75	246.276
203657	6109711 158455369581401 132602900510114310940573183 7639839012609820796998312583	98076477528349072630050524923418149286212793140335 1291303901059100042612479	75	249.117
203657	158455369581401 448821536522329129 135135144122148732391 132602900510114310940573183	12743889051994416095622163326486453996084497662573 00136056142883701278051170137	79	259.460
203657	6109711 448821536522329129 132602900510114310940573183 7639839012609820796998312583	27779958140426507716973831373920703624670750650729 28211720102766494585292073391	79	260.584
203657	158455369581401 448821536522329129 135135144122148732391 7639839012609820796998312583	73423175795745038600882572056588442807968857361364 481523920355628511801691806737	80	265.309
203657	6109711 135135144122148732391 132602900510114310940573183 7639839012609820796998312583	83642346490363412853159893908566450729423370193773 7254232329622086523241475722689	81	268.818
203657	6109711 158455369581401 448821536522329129 135135144122148732391 132602900510114310940573183	77861479123749855957999783119630879330871412298496 55471563712794121419223292748900407	85	282.003
203657	158455369581401 448821536522329129 132602900510114310940573183 7639839012609820796998312583	72047328164902260360212586599508300870789343488677 248663166644675190007759807350852281	86	285.213
203657	6109711 158455369581401 448821536522329129 135135144122148732391 7639839012609820796998312583	44859438481419721553523686020243103149671821547815 9547775992959907430468426250230923007	87	287.851
203657	158455369581401 135135144122148732391 132602900510114310940573183 7639839012609820796998312583	21692644587912805400436407551065450869420079446991 018099666740267302539312553153879846999	89	293.447
203657	448821536522329129 135135144122148732391 132602900510114310940573183 7639839012609820796998312583	61443964321942478367282993200002831979191875446788 341881401688897755913705932344646956494471	92	304.915
203657	6109711 158455369581401 448821536522329129 132602900510114310940573183 7639839012609820796998312583	44018835340971315404765480268546846042157123059554 9761607084543805099817500180329383040600791	93	307.756
203657	6109711 158455369581401 135135144122148732391 132602900510114310940573183 7639839012609820796998312583	13253578925786133419590572401522764689685542301815 4940184732979345281264765838442344393888107289	96	315.990
203657	6109711 448821536522329129 135135144122148732391 132602900510114310940573183 7639839012609820796998312583	37540486470137950144785094366698250257442037252787 2647064560594077197181284185611345301210790907881	99	327.457
203657	158455369581401 448821536522329129 135135144122148732391 132602900510114310940573183 7639839012609820796998312583	97361260751798125072040230801476390717826954612570 22154353847609705939905049853144611437168433917640 933871	106	352.086
203657	6109711 158455369581401 448821536522329129 135135144122148732391 132602900510114310940573183 7639839012609820796998312583	59484916578912927453201999057031912060900524069292 10208369940063334408780322204330601708839378955938 3907721921281	113	374.628

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-05-05T03:32:48	Oliver Kruse	Ollaptop	30000000	3000000000		-	skipped known factor: 6109711 skipped known factor: 158455369581401 skipped known factor: 448821536522329129 skipped known factor: 135135144122148732391	-	-	1.282	-	-	12.376%
2022-02-06T18:22:42	Oliver Kruse	Threadripper-PC	30000000	10264076402580		-	skipped known factor: 6109711 skipped known factor: 158455369581401 skipped known factor: 448821536522329129 skipped known factor: 135135144122148732391	-	-	3,739	-	-	23.172%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-02-27T11:33:00	TJAOI	Manual testing	?	?	158455369581401	47.171	15	5.22076e-5	0.002	0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.595 GHz-days
Estimated T-Level:	28.203

Digits	B1	Curves	Complete	FacMiss
20	11000	691 / 100	6.910	0.096%
25	50000	691 / 280	2.468	8.439%
30	250000	410 / 640	0.641	52.670%

New Calculation Method

Total ECM effort:	11.595 GHz-days
Estimated T-Level:	28.203

Digits	B1	Complete	FacMiss
20	11000	43.231	0.000%
25	50000	5.812	0.299%
30	250000	0.590	55.440%
35	1000000	0.047	95.389%
40	3000000	0.003	99.691%

ECM Summary

B1	B2	factor	curves	GHz-days
		448821536522329129	1	0.00000e+0
		135135144122148732391	1	0.00000e+0
50000	5000000		281	1.372
250000	25000000		348	8.497
250000	25000000	132602900510114310940573183	3	0.073
250000	25000000	7639839012609820796998312583	2	0.049
250000	31250000		15	0.396
250000	38464196		14	0.403
250000	38500000		28	0.806

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-07-28T13:26:00	TJAOI	Manual testing	50000	5000000						50	0.244
2014-07-28T13:45:00	TJAOI	Manual testing			448821536522329129	58.639		1		1	-
2014-07-28T13:45:00	TJAOI	Manual testing			135135144122148732391	66.873		1		1	-
2014-12-12T13:36:00	TJAOI	Manual testing	50000	5000000						50	0.244
2015-07-24T08:17:00	TJAOI	Manual testing	50000	5000000						90	0.439
2016-03-11T13:47:11	TJAOI	Manual testing	50000	5000000						91	0.444
2018-03-23T17:12:53	TJAOI	Manual testing	250000	25000000						44	1.074
2019-06-26T13:41:49	storm5510	M520_Arrandale	250000	25000000						3	0.073
2019-09-11T09:14:59	storm5510	M520_Arrandale	250000	25000000						3	0.073
2019-11-20T06:16:09	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000	7639839012609820796998312583	92.626	2	2	4630006209346984	2	0.049
2019-11-21T00:40:35	ATH	ec2-ECMCF	250000	25000000						3	0.073
2019-11-21T01:44:16	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-21T01:45:25	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-21T01:50:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-21T03:56:05	kracker	O0	250000	25000000						3	0.073
2019-11-21T08:11:45	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-21T21:41:09	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-22T06:00:03	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-22T11:28:49	Ducho_YYZ	Dutch	250000	25000000						3	0.073
2019-11-22T14:38:21	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-23T00:42:53	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-23T10:52:37	ATH	ec2-ECMCF	250000	25000000						3	0.073
2019-11-24T00:15:15	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-24T12:57:19	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-25T02:20:21	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-25T15:43:21	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-26T06:29:08	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-26T20:38:05	ATH	ec2-ECMCF	250000	25000000						3	0.073
2019-11-27T14:37:44	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-28T07:17:12	ATH	ec2-ECMCF	250000	25000000						3	0.073
2019-11-29T03:33:39	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-30T00:12:14	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-30T22:48:19	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-01T23:11:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-03T00:11:24	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-04T03:04:38	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-05T05:33:52	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-06T08:39:12	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-07T11:08:55	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-08T11:27:09	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-09T11:12:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-10T10:59:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-11T11:11:49	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-12T11:33:58	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-13T12:42:59	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-14T14:08:51	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-15T16:08:59	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-16T22:52:26	Ducho_YYZ	oracleKO	250000	25000000						3	0.073
2019-12-17T21:53:43	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-19T09:47:46	Ducho_YYZ	oracleSP2	250000	25000000						3	0.073
2019-12-20T08:34:34	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-21T15:45:37	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-23T00:25:22	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-24T09:06:22	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-26T03:57:19	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-28T02:51:14	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-30T00:49:18	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-31T23:43:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-03T02:40:39	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-05T04:34:14	kracker	O0	250000	25000000						3	0.073
2020-01-07T07:07:22	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-09T12:29:15	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-11T16:39:41	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-13T22:04:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-16T02:19:08	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-18T08:17:50	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-21T12:47:04	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.073
2020-01-23T01:01:33	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-25T09:00:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-27T20:59:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-30T13:01:12	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-02T11:16:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-05T13:37:31	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-08T20:06:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-12T06:28:49	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-16T11:25:04	MarkS	desktop-i7	250000	25000000						3	0.073
2020-02-19T04:23:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-22T16:52:12	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-26T08:24:25	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-29T16:39:29	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-06T08:01:59	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.073
2020-03-11T00:33:58	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-16T20:16:52	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-22T08:24:29	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-04-11T21:21:09	Oliver Kruse	Melissa	250000	25000000						3	0.073
2020-04-28T19:17:30	Greg	azure	250000	25000000						3	0.073
2020-05-02T22:27:15	Greg Hogan	azure	250000	25000000						3	0.073
2020-05-09T12:02:08	Massimo Cappelli (ik5pwa)	maxlinux_8	250000	25000000						3	0.073
2020-05-31T08:31:00	nordi	sweet16	250000	25000000	132602900510114310940573183	86.777	3	2	712576670007140	3	0.073
2020-06-13T22:00:29	Chang Chia-Tche	exbpc13	250000	25000000						3	0.073
2020-06-25T05:56:40	nordi	sweet16	250000	25000000						3	0.073
2020-07-03T14:15:47	kracker	O0	250000	25000000						3	0.073
2020-07-19T00:50:39	-Anonymous-	aws	250000	25000000						3	0.073
2020-07-28T01:55:18	_p95holder_	TFL1_PRPt8pE_n	250000	25000000						3	0.073
2020-09-04T16:18:53	Massimo Cappelli (ik5pwa)	maxlinux_8	250000	25000000						7	0.171
2020-10-19T21:33:31	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.171
2020-11-03T21:15:28	nordi	sweet16	250000	25000000						7	0.171
2020-12-14T13:25:27	Poao	virmach-USny	250000	25000000						7	0.171
2021-01-23T12:59:06	seatsea	dt	250000	38464196						7	0.201
2021-03-06T03:06:20	Deufo	Ryzen2600	250000	38500000						7	0.201
2021-04-29T02:29:24	Chang Chia-Tche	exbpc13	250000	25000000						7	0.171
2021-06-19T21:59:44	Daniil Tsarkov	9900KF	250000	25000000						7	0.171
2021-07-14T09:02:39	seatsea	Manual testing	250000	38464196						7	0.201
2021-09-09T03:37:40	Dylan Delgado	laptop-ryzen73700	250000	38500000						7	0.201
2021-10-16T12:33:09	Dylan Delgado	laptop-i78750	250000	38500000						7	0.201
2021-12-22T06:22:08	JackBlock	school2	250000	25000000						7	0.171
2022-02-26T05:23:59	Dylan Delgado	colab	250000	38500000						7	0.201
2022-05-02T10:36:49	MarkS	desktop-i7	250000	31250000						15	0.396

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