M101 273 Mersenne number exponent details

is 2 ¹⁰¹²⁷³ - 1

has 30487 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	293.4041	74.6269%	1000000000	6737693622660	1,185.8862	25.4997%	1,479.2904	81.0969%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1590%	0.0000	62.9705%
Difference	+23	+293.4041	+13.2632%	+999998800	+6737693604660	+1,185.8862	+21.3406%	+1,479.2903	+18.1264%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101273	9576374881	10	33.157	47280 2⁴ × 3 × 5 × 197	-	16	197	1.394e-8	8.333e-8	1.049e-7
101273	77362750139369	14	46.137	381951508 2² × 587 × 162671	2008-07-26	587	162671	0.0001	3.035e-5	5.334e-5
101273	3271387127383937	16	51.539	16151329216 2⁶ × 11 × 22942229	2010-01-15	64	22942229	0.0050	0.0040	0.0075
101273	13623343641446090328554377	26	83.494	67260492142259488356 2² × 3 × 5605041011854957363	2017-02-24	4	5605041011854957363	38,585,717	983,996,089	1.838e+9

exponent	prime factors	composite factor	digits	bits*
101273	9576374881 77362750139369	740854697159732540790089	24	79.294
101273	9576374881 3271387127383937	31328029512706281529686497	26	84.696
101273	77362750139369 3271387127383937	253083504944951624703121915753	30	97.676
101273	9576374881 13623343641446090328554377	130462245843175409938025172945404137	36	116.651
101273	77362750139369 13623343641446090328554377	1053939330195955304530070292257044968113	40	129.631
101273	9576374881 77362750139369 3271387127383937	2423622519550274026567115796297627400393	40	130.832
101273	3271387127383937 13623343641446090328554377	44567231020554549252977877019779060842249	41	135.033
101273	9576374881 77362750139369 13623343641446090328554377	10092918127786511186100470655934694227924779169553	50	162.788
101273	9576374881 3271387127383937 13623343641446090328554377	42679251166096258015649465594091933841948402714736 9	51	168.190
101273	77362750139369 3271387127383937 13623343641446090328554377	34478435578466968753244812302501862815432867552734 00881	55	181.170
101273	9576374881 77362750139369 3271387127383937 13623343641446090328554377	33017842440980778405678550777723861252141925197380 190484251670161	65	214.327

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-11-02	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 9576374881 skipped known factor: 77362750139369 skipped known factor: 3271387127383937	-	-	0.656	-	-	11.734%
2021-12-18	Seth_Tr	Manual testing	1000000000	6737693622660		-	skipped known factor: 9576374881 skipped known factor: 77362750139369 skipped known factor: 3271387127383937	-	-	1,186	-	-	25.500%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-26	J Feitsma	Manual testing	?	?	77362750139369	46.137	14	4.50406e-5	0.000	9.14453e-5
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	3271387127383937	51.539	16	0.005	0.000	0.010
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	77362750139369	46.137	14	0.000	0.000	0.000
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	9576374881	33.157	10	1.39410e-8	0.000	2.97363e-8
2018-11-02	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.379	-	-
2018-11-02	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.758	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.517	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.033	-	-
2022-12-08	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.69	-	-
2022-12-08	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.39	-	-
2022-12-08	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	36.89	-	-

ECM factoring results:

Total ECM effort:	12.595 GHz-days
Estimated T-Level:	30.756

Digits	B1	Complete	FacMiss
20	11000	82.451	0.000%
25	50000	12.936	0.000%
30	250000	1.545	21.335%
35	1000000	0.151	85.964%
40	3000000	0.013	98.746%

ECM Summary

B1	B2	factor	curves	GHz-days
		3271387127383937	1	0.00000e+0
50000	5000000		280	0.650
250000	25000000		498	5.781
250000	25000000	13623343641446090328554377	87	1.010
1000000	100000000		111	5.154

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-01-15	Rob_Dee	twopc			3271387127383937	51.539		1		1	-
2010-04-20	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2014-04-11	TJAOI	Manual testing	50000	5000000						38	0.088
2014-05-13	TJAOI	Manual testing	50000	5000000						231	0.536
2017-02-25	kkmrkkblmbrbk	kel1	250000	25000000	13623343641446090328554377	83.494	87	2		87	1.010
2017-02-25	kkmrkkblmbrbk	kel1	250000	25000000						498	5.781
2019-01-26	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-19	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-04	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-09	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-14	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-21	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-03	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-09	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-04	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-12	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-17	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-04	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-18	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-17	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-09	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-10-16	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-24	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-31	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-07	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M101273

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

5EBA2B606A5BC3__

2017-09-21

Oliver Kruse

Manual testing

5EBA2B606A5BC3__

2017-10-09

Chang Chia-Tche

homura

5EBA2B606A5BC3__

2017-10-13

kkmrkkblmbrbk

Manual testing

9576374881

77362750139369

3271387127383937

13623343641446090328554377

5EBA2B606A5BC3__

2020-04-17

Oliver Kruse

AddPrpType5

9576374881

77362750139369

3271387127383937

13623343641446090328554377

46A0009C38FADA__

2022-04-15

LordJulius

WhiteBox

9576374881

77362750139369

3271387127383937

13623343641446090328554377

46A0009C38FADA4E

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 = 1000000000, B2 = 6737693622660 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 100000000, B2 = 2000000000 (P-1 stage 2)

B1 = 100000000 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁵

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2⁶³

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this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=30.76 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-04-26T21:34:10+00:00

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