M729 947 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	40.7070	70.1493%	1500000	3613488450	5.7425	11.1106%	46.4494	73.4658%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5791%	0.0010	62.0814%
Difference	+23	+40.7069	+15.6038%	+1488000	+3613038450	+5.7414	-5.4685%	+46.4484	+11.3844%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
729947	618995057	9	29.205	424 2³ × 53	-	8	53	1.070e-10	3.027e-7	4.715e-7
729947	2969044823561	13	41.433	2033740 2² × 5 × 61 × 1667	2008-07-16	61	1667	4.830e-7	4.300e-6	4.903e-6
729947	1522894833919294382445786922681	31	100.265	1043154389235995478059220 2² × 3² × 5 × 263 × 414431 × 619471 × 85831583	2023-01-07	619471	85831583	2.181e+11	0.1524	0.2529

exponent	prime factors	composite factor	digits	bits*
729947	618995057 2969044823561	1837824069795696137977	22	70.638
729947	618995057 1522894833919294382445786922681	942664374526879159661809675614780187817	39	129.470
729947	2969044823561 1522894833919294382445786922681	4521543023475869787842369889499210794087041	43	141.698
729947	618995057 2969044823561 1522894833919294382445786922681	27988127815443983574500656567656476869409232067563 37	52	170.903

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: 618995057 skipped known factor: 2969044823561	-	-	0.037	-	-	4.533%
2023-01-07	USAFSS	6917th_Scty_Sq	1500000	3613488450			1522894833919294382445786922681	31	100.265	5.742	0.029	11.48	11.111%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-16	J Feitsma	Manual testing	?	?	2969044823561	41.433	13	8.16560e-8	0.030	1.69143e-7

ECM factoring results:

Total ECM effort:	11.343 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	6.362
250000	25000000		44	4.981

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-10-30	TJAOI	Manual testing	50000	5000000						100	2.264
2016-07-01	TJAOI	Manual testing	50000	5000000						90	2.038
2017-12-08	TJAOI	Manual testing	50000	5000000						91	2.060
2019-01-25	TJAOI	Manual testing	250000	25000000						44	4.981

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-1

618995057

2969044823561

84F31C595B35FB__

2017-09-28

Oliver Kruse

Manual testing

618995057

2969044823561

84F31C595B35FB__

2017-11-09

kkmrkkblmbrbk

c4.large

618995057

2969044823561

84F31C595B35FB__

2020-04-20

Oliver Kruse

AddPrpType5

618995057

2969044823561

69EF808C217500__

2023-01-08

LordJulius

WhiteBox

618995057

2969044823561

1522894833919294382445786922681

69EF808C2175006D

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 = 3613488450 (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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=25.66 ~= 69-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

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