M721 111 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	41.2057	70.1493%	1650000	3618231540	5.7540	11.2135%	46.9598	73.4966%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5561%	0.0010	62.0709%
Difference	+23	+41.2057	+15.6038%	+1638000	+3617781540	+5.7530	-5.3426%	+46.9588	+11.4256%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
721111	670633231	9	29.321	465 3 × 5 × 31	-	5	31	1.092e-10	1.858e-7	2.947e-7
721111	263310797207	12	37.938	182573 41 × 61 × 73	2008-07-16	61	73	3.854e-8	1.785e-6	3.595e-6
721111	3059305992147642685477621832879	31	101.271	2121244851449806399762049 11 × 53 × 1747 × 12329 × 170111 × 993045371	2023-01-02	170111	993045371	2.075e+11	1.5715	2.9264

exponent	prime factors	composite factor	digits	bits*
721111	670633231 263310797207	176584970688116185817	21	67.259
721111	670633231 3059305992147642685477621832879	2051672262131634243195374307979785802049	40	130.592
721111	263310797207 3059305992147642685477621832879	805548299692547877558894966373838013968953	42	139.209
721111	670633231 263310797207 3059305992147642685477621832879	54022745894936968974951412408892334117862208407714 3	51	168.530

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: 670633231 skipped known factor: 263310797207	-	-	0.037	-	-	4.526%
2023-01-02	USAFSS	6917th_Scty_Sq	1650000	3618231540			3059305992147642685477621832879	31	101.271	5.754	0.029	11.51	11.213%

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	?	?	263310797207	37.938	12	1.31514e-8	0.030	2.72541e-8

ECM factoring results:

Total ECM effort:	11.330 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	6.355
250000	25000000		44	4.975

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-10-16	TJAOI	Manual testing	50000	5000000						100	2.262
2016-06-24	TJAOI	Manual testing	50000	5000000						90	2.035
2016-12-09	TJAOI	Manual testing	50000	5000000						91	2.058
2018-11-23	TJAOI	Manual testing	250000	25000000						44	4.975

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-2

670633231

263310797207

E3667A40E1A020__

2017-09-28

Oliver Kruse

Manual testing

670633231

263310797207

E3667A40E1A020__

2017-11-09

kkmrkkblmbrbk

c4.large

670633231

263310797207

E3667A40E1A020__

2020-04-20

Oliver Kruse

AddPrpType5

670633231

263310797207

5A9E7A58B77DC9__

2023-01-02

LordJulius

WhiteBox

670633231

263310797207

3059305992147642685477621832879

5A9E7A58B77DC9D7

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 = 1650000, B2 = 3618231540 (P-1 stage 2)

B1 = 1650000 (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