M8 573 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	3,465.9883	79.1045%	400000000	400000000	0.0707	7.5247%	3,466.0590	80.6768%
Target	2⁴⁴	0.0003	68.1818%	500	10000	0.0000	1.2053%	0.0003	68.5653%
Difference	+23	+3,465.9880	+10.9227%	+399999500	+399990000	+0.0707	+6.3195%	+3,466.0587	+12.1115%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8573	12345121	8	23.557	720 2⁴ × 3² × 5	-	16	16	1.507e-10	2.829e-9	5.758e-9
8573	12254091887	11	33.513	714691 714691	-	1	714691	2.263e-7	6.885e-6	1.286e-5
8573	21973130527	11	34.355	1281531 3 × 19 × 22483	-	19	22483	3.705e-7	2.198e-7	4.045e-7
8573	64052833558423	14	45.864	3735730407 3 × 1245243469	-	3	1245243469	0.0009	0.0120	0.0224
8573	79764519978606583742551	23	76.078	4652077451219327175 3 × 5² × 71 × 873629568304099	1999-10-07	71	873629568304099	2,903,761	8,416.2	15,719

exponent	prime factors	composite factor	digits	bits*
8573	12345121 12254091887	151278247090133327	18	57.070
8573	12345121 21973130527	271260955104608767	18	57.912
8573	12254091887 21973130527	269260760522902734449	21	67.868
8573	12345121 64052833558423	790739980671592504183	21	69.422
8573	12254091887 64052833558423	784909308047632624814201	24	79.377
8573	21973130527 64052833558423	1407441272403434459278921	25	80.219
8573	12345121 12254091887 21973130527	3324056669207257528003773329	28	91.425
8573	12345121 79764519978606583742551	984702650642815687698424943671	30	99.636
8573	12345121 12254091887 64052833558423	9689800381874298516878913863321	31	102.934
8573	12345121 21973130527 64052833558423	17375032808214359215367852494441	32	103.777
8573	12254091887 79764519978606583742551	977441757140292351404380305783737	33	109.591
8573	21973130527 79764519978606583742551	1752676208913421712156629286954377	34	110.433
8573	12254091887 21973130527 64052833558423	17246914677587883198386057696213927	35	113.732
8573	64052833558423 79764519978606583742551	5109143522057193621175558510249557073	37	121.942
8573	12345121 12254091887 79764519978606583742551	12066636762349523053461594804917233097177	41	133.148
8573	12345121 21973130527 79764519978606583742551	21636999872857469560600759499595505544617	41	133.991
8573	12345121 12254091887 21973130527 64052833558423	212915248571498406217942886972742170700167	42	137.289
8573	12254091887 21973130527 79764519978606583742551	21477455312183878088348200218534226134839399	44	143.946
8573	12345121 64052833558423 79764519978606583742551	63072994986162224173840432051610522262590833	44	145.500
8573	12254091887 64052833558423 79764519978606583742551	62607914183159661903235562943142903673592766751	47	155.455
8573	21973130527 64052833558423 79764519978606583742551	112263877491339218997402338327839184908965067471	48	156.298
8573	12345121 12254091887 21973130527 79764519978606583742551	26514178460100274924990722183003146427595469622227 9	51	167.503
8573	12345121 12254091887 64052833558423 79764519978606583742551	77290227614872218851453331603621526614184721026587 1871	54	179.012
8573	12345121 21973130527 64052833558423 79764519978606583742551	13859111515597591105684305523401124062425477427026 58991	55	179.855
8573	12254091887 21973130527 64052833558423 79764519978606583742551	13756918703697818362809842681780033020336416668627 88707777	58	189.810
8573	12345121 12254091887 21973130527 64052833558423 79764519978606583742551	16983082598431271512490940789753900302004852448062 816994940706017	65	213.367

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-27	Seth_Tr	Manual testing	100000000	100000000		-	skipped known factor: 12345121 skipped known factor: 12254091887 skipped known factor: 21973130527	-	-	0.018	-	-	5.582%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 12345121 skipped known factor: 12254091887 skipped known factor: 21973130527	-	-	0.071	-	-	7.525%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-10-07	Alex Kruppa	v4_computers	?	?	12345121 21973130527 79764519978606583742551	133.991	41	4.53140e+12	2.27079e-6	9.84269e+12
1999-10-07	Alex Kruppa	v4_computers	?	?	79764519978606583742551	76.078	23	1,118,623	2.27079e-6	2,429,771

ECM factoring results:

Total ECM effort:	2,345.612 GHz-days
Estimated T-Level:	46.144

Digits	B1	Complete	FacMiss
20	11000	4,383.800	0.000%
25	50000	1,234.835	0.000%
30	250000	329.253	0.000%
35	1000000	67.592	0.000%
40	3000000	11.654	0.001%
45	11000000	1.742	17.515%
50	44000000	0.229	79.550%
55	110000000	0.027	97.336%
60	260000000	0.003	99.720%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		3,919	29.91
11000000	36578884662		7,200	2,316

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.008
2013-04-18	Axon		3000000	300000000						30	0.229
2017-12-03	James Hintz	10_12_2017	3000000	300000000						1000	7.633
2018-03-17	James Hintz	3_1_2018	3000000	300000000						2888	22.04
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

C1A3EC701049A1__

2017-09-21

Oliver Kruse

Manual testing

C1A3EC701049A1__

2017-10-02

kkmrkkblmbrbk

Manual testing

12345121

12254091887

21973130527

64052833558423

79764519978606583742551

C1A3EC701049A1__

2017-12-07

ATH

Manual testing

12345121

12254091887

21973130527

64052833558423

79764519978606583742551

C1A3EC701049A1__

2020-04-17

Oliver Kruse

Manual testing

12345121

12254091887

21973130527

64052833558423

79764519978606583742551

3F75ABA92AD181__

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 = 400000000 (P-1 stage 1)

B1 = 100000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=46.14 ~= 137-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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