M735 557 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	40.3965	70.1493%	2000000	5219492850	8.2901	11.8850%	48.6866	73.6970%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5935%	0.0010	62.0880%
Difference	+23	+40.3965	+15.6038%	+1988000	+5219042850	+8.2891	-4.7085%	+48.6856	+11.6091%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
735557	21875683299130553	17	54.280	14870148268 2² × 17 × 71 × 167 × 18443	2000-05-31	167	18443	0.0059	3.367e-5	5.435e-5
735557	192293780198976939871	21	67.382	130713038009955 3² × 5 × 2904734177999	2015-10-23	9	2904734177999	45.278	4,583.1	8,560.0
735557	27977609972503934772560177	26	84.532	19017975474710956984 2³ × 7351 × 210869 × 1533610717	2023-01-14	210869	1533610717	8,443,836	2.4255	4.5194

exponent	prime factors	composite factor	digits	bits*
735557	21875683299130553 192293780198976939871	4206557836025441270308478950859978663	37	121.662
735557	21875683299130553 27977609972503934772560177	612029335225092736030620333667745971787881	42	138.813
735557	192293780198976939871 27977609972503934772560177	5379920382545376899522242105349672399658117167	46	151.914
735557	21875683299130553 192293780198976939871 27977609972503934772560177	11768943446309995729624155929339575434190204280071 9660103503351	63	206.195

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: 21875683299130553	-	-	0.037	-	-	4.537%
2023-01-14	USAFSS	6917th_Scty_Sq	2000000	5219492850			27977609972503934772560177	26	84.532	8.290	0.029	16.58	11.885%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-05-31	ANONYMOUS	v4_computers	?	?	21875683299130553	54.280	17	0.003	0.030	0.005
2003-08-25	ANONYMOUS	v4_computers	?	?	21875683299130553	54.280	17	0.003	0.030	0.005

ECM factoring results:

Total ECM effort:	11.351 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		269	6.095
50000	5000000	192293780198976939871	12	0.272
250000	25000000		44	4.985

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-10-23	TJAOI	Manual testing	50000	5000000						88	1.994
2015-10-23	TJAOI	Manual testing	50000	5000000	192293780198976939871	67.382	12	2		12	0.272
2016-07-22	TJAOI	Manual testing	50000	5000000						90	2.039
2017-04-14	TJAOI	Manual testing	50000	5000000						91	2.062
2019-01-18	TJAOI	Manual testing	250000	25000000						44	4.985

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-3

21875683299130553

192293780198976939871

6C0B0B7F4E7B95__

2017-09-28

Oliver Kruse

Manual testing

21875683299130553

192293780198976939871

6C0B0B7F4E7B95__

2017-11-09

kkmrkkblmbrbk

c4.large

21875683299130553

192293780198976939871

6C0B0B7F4E7B95__

2020-04-20

Oliver Kruse

AddPrpType5

21875683299130553

192293780198976939871

CF0D80E120ABC4__

2023-01-15

LordJulius

WhiteBox

21875683299130553

192293780198976939871

27977609972503934772560177

CF0D80E120ABC4F1

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 = 2000000, B2 = 5219492850 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

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

B1 = 500000 (P-1 stage 1)

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10⁷

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10⁹

10¹⁰

10¹¹

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10¹³

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