M8 243 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	unknown	-	-	-	-	0.0000	0.0000%
Target	2⁴⁴	0.0003	68.1818%	500	80000	0.0000	1.1907%	0.0003	68.5607%
Difference	-44	-0.0003	-68.1818%	-500	-80000	0.0000	-1.1907%	-0.0003	-68.5607%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8243	16487	5	14.009	1 1	-	1	1	2.648e-13	1.474e-10	3.000e-10
8243	4207243687	10	31.970	255201 3 × 257 × 331	-	257	331	4.298e-8	3.848e-8	7.710e-8
8243	228591793996490954574648885834108681199807	42	137.392	13865813053287089322737406638002467621 3 × 7 × 11 × 193 × 1831 × 7333 × 12363585253 × 1873534067187773	2017-10-10	12363585253	1873534067187773	1.986e+13	15,049	28,105
8243	hide decimal representation P2427 click to show decimal representation	2,427	8,059.629		2017-10-10

exponent	prime factors	composite factor	digits	bits*
8243	16487 4207243687	69364826667569	14	45.979
8243	16487 228591793996490954574648885834108681199807	3768792907620146368072236180746949826941218009	46	151.401
8243	4207243687 228591793996490954574648885834108681199807	96174138219174106878679529516713747824978358636840 9	51	169.362
8243	16487 4207243687 228591793996490954574648885834108681199807	15856230168195235001087894031420595603904181988455 959183	56	183.371

ECM factoring results:

Total ECM effort:	22.112 GHz-days
Estimated T-Level:	38.718

Digits	B1	Complete	FacMiss
20	11000	939.933	0.000%
25	50000	221.561	0.000%
30	250000	40.608	0.000%
35	1000000	6.032	0.240%
40	3000000	0.744	47.541%
45	11000000	0.080	92.351%
50	44000000	0.007	99.259%

ECM Summary

B1	B2	factor	curves	GHz-days
1000000	100000000	228591793996490954574648885834108681199807	2,450	5.197
3000000	300000000		2,658	16.92

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.006
2013-04-18	Axon		3000000	300000000						30	0.191
2017-10-10	YarBer	Manual testing	1000000	100000000	228591793996490954574648885834108681199807	137.392	2450	2		2450	5.197
2017-10-10	James Hintz	11_04_2016	3000000	300000000						2627	16.72

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

16487

4207243687

22A4518B19A1D3__

2017-09-21

Oliver Kruse

Manual testing

16487

4207243687

22A4518B19A1D3__

2017-10-10

YarBer

Manual testing

16487

4207243687

228591793996490954574648885834108681199807

PRP

2017-10-12

kkmrkkblmbrbk

c4.xlarge

PRP

2017-11-09

kkmrkkblmbrbk

c4.large

16487

4207243687

228591793996490954574648885834108681199807

PRP

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

10¹

10²

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10⁶

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10⁸

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10¹⁰

10¹¹

10⁰

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10³

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10⁶

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10¹³

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10¹⁶

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=38.72 ~= 112-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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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