M1878697 Mersenne number exponent details

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M1878697

<<<

>>>

is 2 ^1878697 - 1

has 565545 decimal digits

takes 0.102 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	15.8162	68.6567%	500000	15000000	0.1015	5.0846%	15.9177	70.2504%	1.5937%
PrimeNet	2⁵⁷	0.0102	63.1579%	9000	160000	0.0014	3.0317%	0.0116	64.2748%	1.1169%
GPU72	2⁶¹	0.1635	65.5738%	10000	150000	0.0014	1.6912%	0.1649	66.1560%	0.5822%
Difference	+6	+15.6527	+3.0829%	+490000	+14850000	+0.1001	+3.3934%	+15.7528	+4.0944%	+4.0944%

Known prime factors (4 factors, 144.0 bits, 0.00766426% 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
1878697	86420063	8	26.365	23 23	-	1	23	4.782e-12	1.729e-7	1.729e-7
1878697	7078930297	10	32.721	1884 2² × 3 × 157	2008-07-15	4	157	4.288e-10	9.704e-7	1.268e-6
1878697	1516435372279	13	40.464	403587 3² × 44843	2008-07-15	9	44843	1.058e-7	0.0002	0.0004
1878697	23844046584601	14	44.439	6345900 2² × 3² × 5² × 11 × 641	2014-01-10	25	641	1.960e-6	4.607e-6	5.127e-6

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1878697	86420063 7078930297	611761602239348711	18	59.086
1878697	86420063 1516435372279	131050440407779633577	21	66.829
1878697	86420063 23844046584601	2060604008016153249863	22	70.804
1878697	7078930297 1516435372279	10734740300268287036863	23	73.185
1878697	7078930297 23844046584601	168790343770811392556497	24	77.160
1878697	1516435372279 23844046584601	36157955659157235903675679	26	84.903
1878697	86420063 7078930297 1516435372279	927696933037824282627783782369	30	99.550
1878697	86420063 7078930297 23844046584601	14586872142465178105850201799311	32	103.524
1878697	86420063 1516435372279 23844046584601	3124772806015574853701514110747777	34	111.267
1878697	7078930297 1516435372279 23844046584601	255959647793190762725305937735146663	36	117.623
1878697	86420063 7078930297 1516435372279 23844046584601	22120048887745356685738990833345451930699769	44	143.988

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:39:08	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 86420063 skipped known factor: 7078930297 skipped known factor: 1516435372279 skipped known factor: 23844046584601	-	-	0.101	-	-	5.085%

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	?	?	1516435372279	40.464	13	2.77945e-8	0.217	5.93074e-8
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	7078930297	32.721	10	1.24195e-10	0.217	2.65006e-10
2014-01-10T14:40:00	TJAOI	Manual testing	?	?	23844046584601	44.439	14	7.12834e-7	0.217	1.52102e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.827 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:	19.827 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.628	0.002%
25	50000	0.978	37.597%
30	250000	0.062	93.981%
35	1000000	0.003	99.709%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	38	2.632
50000	6600000	213	16.64
50000	6721097	7	0.552

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-04-05T11:53:07	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-22T05:23:29	BanWaiLun	asia-northeast1-b	50000	5000000						3	0.208
2020-07-05T04:17:25	kracker	O0	50000	5000000						3	0.208
2020-08-06T16:00:01	Ahmed Azhad	c5.xlarge.az	50000	5000000						3	0.208
2020-10-12T12:26:29	nordi	sweet16	50000	5000000						7	0.485
2020-12-14T05:10:15	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.485
2021-03-18T05:28:21	Kublenz	Medion_E4272	50000	5000000						7	0.485
2021-07-11T00:29:13	MarkS	desktop-i7	50000	5000000						7	0.485
2021-09-23T15:19:47	Ahmed Azhad	c5.4xlarge.azf	50000	6721097						7	0.552
2021-10-20T13:17:49	TJAOI	Manual testing	50000	6600000						213	16.64

Lucas-Lehmer results:
No L-L results for M1878697

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T13:15:11

Oliver Kruse

GTX-3

86420063

7078930297

1516435372279

23844046584601

E2E7797B5E3F3E16

2017-10-05T21:45:35

Oliver Kruse

Manual testing

86420063

7078930297

1516435372279

23844046584601

E2E7797B5E3F3E__

2017-11-11T04:15:32

kkmrkkblmbrbk

c4.xlarge

86420063

7078930297

1516435372279

23844046584601

E2E7797B5E3F3E__

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

B1 = 500000 (P-1 stage 1)

10⁰

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10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

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10⁸

TF factor-bounds graph:

2⁶⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-10-20T13:17:49+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