M709 321 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	1500000	4299875580	6.8254	45.4849%	6.8254	45.4849%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5250%	0.0010	62.0568%
Difference	-44	0.0000	-54.5455%	+1488000	+4299425580	+6.8244	+28.9600%	+6.8244	-16.5719%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
709321	629877049	9	29.230	444 2² × 3 × 37	-	4	37	1.105e-10	1.679e-7	2.358e-7
709321	137676087235202974155665940799	30	96.797	97047801513844207457319 3² × 7² × 3691 × 15107 × 28703 × 137498369	2022-12-26	28703	137498369	3.075e+10	0.2177	0.4052

exponent	prime factors	composite factor	digits	bits*
709321	629877049 137676087235202974155665940799	86719007545576218277194129420282822151	38	126.028

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 629877049	-	-	0.037	-	-	29.445%
2022-12-26	USAFSS	6917th_Scty_Sq	1500000	4299875580			137676087235202974155665940799	30	96.797	6.825	0.028	13.65	45.485%

ECM factoring results:

Total ECM effort:	11.313 GHz-days
Estimated T-Level:	25.658

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	6.345
250000	25000000		44	4.968

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-10-30	TJAOI	Manual testing	50000	5000000						100	2.258
2016-05-20	TJAOI	Manual testing	50000	5000000						90	2.032
2017-01-27	TJAOI	Manual testing	50000	5000000						91	2.055
2018-10-12	TJAOI	Manual testing	250000	25000000						44	4.968

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-3

629877049

2B8DD2C8CD240F__

2017-09-28

Oliver Kruse

Manual testing

629877049

2B8DD2C8CD240F__

2017-11-09

kkmrkkblmbrbk

c4.large

629877049

2B8DD2C8CD240F__

2020-04-20

Oliver Kruse

AddPrpType5

629877049

80E65EE57FFBC5__

2022-12-26

LordJulius

WhiteBox

629877049

137676087235202974155665940799

80E65EE57FFBC55B

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 = 1500000, B2 = 4299875580 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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