M827 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	35,929.7673	85.0746%	-	-	-	-	35,929.7673	85.0746%
Target	2⁴⁴	0.0028	77.2727%	500	80000	0.0000	0.5686%	0.0028	77.4019%
Difference	+23	+35,929.7644	+7.8019%	-500	-80000	0.0000	-0.5686%	+35,929.7644	+7.6727%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
827	66161	5	16.014	40 2³ × 5	-	8	8	1.065e-11	1.531e-10	3.115e-10
827	1637241673	10	30.609	989868 2² × 3 × 11 × 7499	-	11	7499	2.174e-7	8.016e-9	1.460e-8
827	1656489332706171370072190422631	31	100.386	1001505037911832750950538345 5 × 19 × 10902209 × 966974518082414839	2005-01-20	10902209	966974518082414839	2.303e+14	1,007,937	1,882,545
827	2550707823005230793212015514781257	34	110.975	1542144995770998061192270565164 2² × 173 × 1249 × 1784253987896673478889783	2005-01-20	1249	1784253987896673478889783	1.986e+14	1.860e+12	3.474e+12
827	13394595223843413901037846777300844745495137348727 969920754613220161097793251799	80	262.854	80983042465800567720905966005446461580986320125320 25345075340520049031313937 3 × 101 × 1297 × 20606844041161392429064779093019041550820838168131141285870008524493007	2009-04-12	1297	20606844041161392429064779093019041550820838168131141285870008524493007	1.622e+14	2.148e+58	4.012e+58
827	hide decimal representation P93 click to show decimal representation	93	306.163		2009-04-12

exponent	prime factors	composite factor	digits	bits*
827	66161 1637241673	108321546327353	15	46.622
827	66161 1656489332706171370072190422631	109594990741173004015346190551689591	36	116.400
827	66161 2550707823005230793212015514781257	168757380277849074509700158473442744377	39	126.988
827	1637241673 1656489332706171370072190422631	2712073366386505631361695178322955501663	40	130.995
827	1637241673 2550707823005230793212015514781257	4176125143471271951629557325122421439722961	43	141.583
827	66161 1637241673 1656489332706171370072190422631	179433485993497599076521114693025058945525743	45	147.008
827	66161 1637241673 2550707823005230793212015514781257	276296615617202823591763142187424524873510822721	48	157.597
827	1656489332706171370072190422631 2550707823005230793212015514781257	42252202996583458271790597366133017860703302720114 77970347427167	64	211.360
827	66161 1656489332706171370072190422631 2550707823005230793212015514781257	27954480024569581827199377123407265946819912112655 1393996156128795887	69	227.374
827	1637241673 1656489332706171370072190422631 2550707823005230793212015514781257	69177067522061914505032126337397015702796756302106 17267374266046144730391	73	241.969
827	66161 1637241673 1656489332706171370072190422631 2550707823005230793212015514781257	45768239643271383255674305106085239559127361937036 4649026748815878981507398951	78	257.983
827	66161 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	88619981460470410710656498063300118920670378212919 1217927045965259078391099332273639	84	278.868
827	1637241673 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	21930189493443200465366660693985693475427717886196 165894949960371044473080540183505019727	89	293.463
827	66161 1637241673 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	14509232670756955859891236381747874660277732430686 24531775784328108673383481619080875610158047	94	309.476
827	1656489332706171370072190422631 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	22188004104213646826313618665002799853759355080505 81773324691006380116744626155178947923715439439882 9611063169	110	363.240
827	2550707823005230793212015514781257 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	34165698823445896322178759158135982713038186893474 54191279932362079227955564562263345547112943055167 5072206731343	113	373.828
827	66161 1656489332706171370072190422631 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	14679805395388790876757353244952502411245726914813 45407049348816731149039412110527943735809371887820 965897550324209	115	379.254
827	66161 2550707823005230793212015514781257 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	22604367998580039465716688846614347522773194830591 69167492716050075238007681070039052047425394254729 374452269552384223	118	389.842
827	1637241673 1656489332706171370072190422631 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	36327124960113617479344849445773210582253121851408 39471181423875493836012907040064738313003742444484 1621659002122241737	119	393.849
827	1637241673 2550707823005230793212015514781257 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	55937505900912690919508498649130627898593720022358 93178422018471817436936516893579552530132295207596 1808172144625874856839	122	404.437
827	66161 1637241673 1656489332706171370072190422631 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	24034389144860770460509345841818013853324487948110 30802528341850265476844499426777231515266406038695 166530581239409635561657	124	409.862
827	66161 1637241673 2550707823005230793212015514781257 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	37008813279102845439256017791251314723988591103992 89285775791641139134451568941961167749460827832297 709190477260592506403325079	127	420.451
827	1656489332706171370072190422631 2550707823005230793212015514781257 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	56595115645489917084493762506708510816345800618782 29074724265186322383552498102512452593063268991634 6071550437162615037058655841287454244223433	143	474.214
827	66161 1656489332706171370072190422631 2550707823005230793212015514781257 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	37443894462212584042271918212063417841202545147392 55138128321089922752182168269603263760096589397555 372439848473115773466837729115419260252066550713	148	490.228
827	1637241673 1656489332706171370072190422631 2550707823005230793212015514781257 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	92659881823050386752047850084548115972292594351619 55292578797947350115964839676686813386800094718712 86722322154440012163288706887206940607233240307234 09	152	504.823
827	66161 1637241673 1656489332706171370072190422631 2550707823005230793212015514781257 13394595223843413901037846777300844745495137348727 969920754613220161097793251799	61304704412948366379022378094437879008428503348975 01241123058509946310223497578492762604840810666847 62008355560599056447353441363644983975151584119669 1462849	157	520.837

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-08-01	ANONYMOUS	v4_computers	?	?	66161 1637241673	46.622	15	0.009	4.12920e-8	0.036
2005-01-20	ANONYMOUS	v4_computers	?	?	66161 1637241673	46.622	15	0.009	4.12920e-8	0.036
2005-01-20	ANONYMOUS	v4_computers	?	?	1656489332706171370072190422631	100.386	31	7.50142e+13	4.12920e-8	2.83866e+14
2005-01-20	ANONYMOUS	v4_computers	?	?	2550707823005230793212015514781257	110.975	34	4.34125e+13	4.12920e-8	1.64280e+14
2005-04-02	Gerry Snyder	v4_computers	?	?	66161 1637241673	46.622	15	0.009	4.12920e-8	0.036
2005-04-02	Gerry Snyder	v4_computers	?	?	1656489332706171370072190422631	100.386	31	7.50142e+13	4.12920e-8	2.83866e+14
2005-04-02	Gerry Snyder	v4_computers	?	?	2550707823005230793212015514781257	110.975	34	4.34125e+13	4.12920e-8	1.64280e+14
2009-04-22	Never Odd Or Even	v4_computers	?	?	66161 1637241673	46.622	15	0.009	4.12920e-8	0.036

ECM factoring results:

Total ECM effort:	0.006 GHz-days
Estimated T-Level:	25.449

Digits	B1	Complete	FacMiss
20	11000	15.385	0.000%
25	50000	1.423	24.087%
30	250000	0.090	91.413%
35	1000000	0.004	99.581%

ECM Summary

B1	B2	factor	curves	GHz-days
		13394595223843413901037846777300844745495137348727 969920754613220161097793251799	1	0.00000e+0
50000	5000000		400	0.006

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-16	Alexander D	Manual testing	50000	5000000						400	0.006
2009-04-12	ANONYMOUS	Manual testing			13394595223843413901037846777300844745495137348727 969920754613220161097793251799	262.854		1		1	-

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

10⁰

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TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=25.45 ~= 68-bit

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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