M4 022 783 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	7.3864	67.1642%	400000000	64400000000	702.9344	21.7856%	710.3209	74.3177%
Target	2⁶⁵	1.8136	66.1538%	22000	2880000	0.0321	1.7510%	1.8457	66.7465%
Difference	+2	+5.5728	+1.0103%	+399978000	+64397120000	+702.9023	+20.0346%	+708.4751	+7.5712%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4022783	8045567	7	22.940	1 1	-	1	1	1.389e-13	1.808e-7	3.681e-7
4022783	278820445327511815240846830394938314849	39	127.713	34655168490011991106759528216528 2⁴ × 7 × 31 × 80111 × 1019467 × 3712259 × 32921885803	2022-06-28	3712259	32921885803	4.507e+10	325.02	605.85

exponent	prime factors	composite factor	digits	bits*
4022783	8045567 278820445327511815240846830394938314849	2243268573852333252811854310680112672984724383	46	150.652

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-06-28	onlinegame	Manual testing	400000000	64400000000			278820445327511815240846830394938314849	39	127.713	702.9	1.003	1,406	21.786%

ECM factoring results:

Total ECM effort:	0.540 GHz-days
Estimated T-Level:	0.577

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.540

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-26	rucio		50000	5000000						3	0.540

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-12

kkmrkkblmbrbk

c4.xlarge

8045567

38EA196FAA85CA__

2018-01-05

Meracayn

8045567

38EA196FAA85CA__

2022-06-29

onlinegame

Manual testing

8045567

278820445327511815240846830394938314849

38EA196FAA85CA96

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, B2 = 64400000000 (P-1 stage 2)

B1 = 400000000 (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

TF factor-bounds graph:

this exponent TF target: 65

TF double-checked to: 67.9

ECM T-Level=0.58 ~= -15-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

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