M1842779 Mersenne number exponent details

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M1842779

<<<

>>>

is 2 ^1842779 - 1

has 554732 decimal digits

takes 0.100 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	16.1245	68.6567%	1000000	188329050	0.8815	8.2209%	17.0060	71.2334%	2.5767%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8829%	0.0117	64.2200%	1.0621%
GPU72	2⁶¹	0.1667	65.5738%	9000	140000	0.0013	1.5969%	0.1680	66.1235%	0.5497%
Difference	+6	+15.9578	+3.0829%	+991000	+188189050	+0.8802	+6.6240%	+16.8381	+5.1099%	+5.1099%

Known prime factors (4 factors, 201.9 bits, 0.01095617% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1842779	1242033047	10	30.210	337 337	-	1	337	8.329e-11	1.519e-6	2.709e-6
1842779	1855608427399	13	40.755	503481 3 × 11² × 19 × 73	2008-07-15	121	121	1.573e-7	9.518e-6	1.937e-5
1842779	428231121391773943	18	58.571	116191665249 3 × 11 × 37 × 95161069	2015-09-15	37	95161069	0.0228	0.4078	0.7617
1842779	6067832966295855252143	22	72.362	1646381081588149 2347 × 20431 × 34334257	2021-03-01	20431	34334257	672.77	0.1487	0.2748

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1842779	1242033047 1855608427399	2304726989121258254753	22	70.965
1842779	1242033047 428231121391773943	531877204522451871159494321	27	88.781
1842779	1855608427399 428231121391773943	794629277729099914545135464257	30	99.326
1842779	1242033047 6067832966295855252143	7536449067815489402290123569721	31	102.572
1842779	1855608427399 6067832966295855252143	11259521988308061334600806854666057	35	113.117
1842779	1242033047 1855608427399 428231121391773943	986955823053283207429934219698881301079	39	129.536
1842779	428231121391773943 6067832966295855252143	2598434915574848158950047858992322309849	40	130.933
1842779	1242033047 1855608427399 6067832966295855252143	13984698402901759794077126666359368943185679	44	143.327
1842779	1242033047 428231121391773943 6067832966295855252143	3227342035622616415423068263100060428107831579903	49	161.143
1842779	1855608427399 428231121391773943 6067832966295855252143	48216777273884973243075086946205301021938460991527 51	52	171.688
1842779	1242033047 1855608427399 428231121391773943 6067832966295855252143	59886830794003706844610021889585295115830440551797 55442962297	61	201.898

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-03T12:49:08	Jocelyn Larouche	Manual testing	1000000	188329050		-	skipped known factor: 1242033047 skipped known factor: 1855608427399 skipped known factor: 428231121391773943 skipped known factor: 6067832966295855252143	-	-	0.882	-	-	8.221%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	1855608427399	40.755	13	7.77827e-8	0.214	1.66271e-7
2015-09-15T11:39:00	TJAOI	Manual testing	2⁵⁸	2⁵⁹*	428231121391773943	58.571	18	0.002	0.203	0.004

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.772 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.772 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.812	0.015%
25	50000	0.798	45.010%
30	250000	0.049	95.182%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	2.488
50000	5000000	6067832966295855252143	2	0.138
50000	6600000		220	17.15

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T06:50:09	alpertron	laptop2	50000	5000000						3	0.207
2019-01-13T09:54:35	pew	desktop	50000	5000000						3	0.207
2020-05-31T04:43:46	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-06-29T03:55:02	-Anonymous-	aws-nano	50000	5000000						3	0.207
2020-07-26T07:18:23	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-10-05T11:01:07	nordi	sweet16	50000	5000000						7	0.484
2020-12-01T12:07:08	nordi	sweet16	50000	5000000						7	0.484
2021-03-01T06:15:46	MarkS	laptop64	50000	5000000	6067832966295855252143	72.362	2	2	6510211157819993	2	0.138
2021-04-11T09:22:46	Chang Chia-Tche	exbpc13	50000	5000000						7	0.484
2021-06-04T15:56:58	TJAOI	Manual testing	50000	6600000						220	17.15

Lucas-Lehmer results:
No L-L results for M1842779

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:28:29

alpertron

Manual testing

1242033047

1855608427399

428231121391773943

55E40B6D603299__

2017-10-19T20:37:07

Oliver Kruse

Threadripper

1242033047

1855608427399

428231121391773943

55E40B6D603299__

2021-03-02T11:12:26

Kriesel

martin

1242033047

1855608427399

428231121391773943

6067832966295855252143

5CE1217FEF83A6CA

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 = 1000000, B2 = 188329050 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁵⁹

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-03T12:49:08+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