M8233 Mersenne number exponent details

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M8233

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is 2 ⁸²³³ - 1

has 2479 decimal digits

takes 0.000 GHz-days to do one PRP test

Has been fully factored.

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- L-L 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	3,609.1240	79.1045%	-	-	-	-	3,609.1240	79.1045%	0.0000%
PrimeNet	2⁴⁰	0.0000	65.0000%	500	10000	0.0000	2.9173%	0.0000	66.0211%	1.0211%
GPU72	2⁴⁴	0.0003	68.1818%	500	10000	0.0000	1.1903%	0.0003	68.5605%	0.3787%
Difference	+23	+3,609.1237	+10.9227%	-500	-10000	0.0000	-1.1903%	+3,609.1237	+10.5439%	+10.5439%

Known prime factors (3 factors, 8,233.0 bits, 100.00000000% known):

Remaining cofactor is a certified-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8233	195611422708913289323830429299939553967	39	127.201	11879717157106357908649971413818751 13 × 23 × 307 × 11847877 × 10923353791203074365891	-	11847877	10923353791203074365891	2.128e+13	8.773e+10	1.639e+11
8233	20866399143857514113654051017725144974702596369	47	153.870	1267241536733724894549620491784595224991048 2³ × 3 × 463 × 19325176312669 × 5901245766232963702257041	2021-03-20	19325176312669	5901245766232963702257041	1.821e+13	4.740e+13	8.852e+13
8233	hide decimal representation P2394 click to show decimal representation	2,394	7,951.929				2021-03-20

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
8233	195611422708913289323830429299939553967 20866399143857514113654051017725144974702596369	40817060233420185545729280060114458912112182745589 89814831525965299820554394693745823	85	281.071

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-02-11T00:00:00	ANONYMOUS	v4_computers	1000000	100000000		-		-	-	0.001	-	-	4.082%
2001-06-23T00:00:00	ANONYMOUS	v4_computers	43000000	4290000000		-		-	-	0.040	-	-	10.255%
2001-08-31T00:00:00	ANONYMOUS	v4_computers	3000000000	4290000000		-		-	-	0.453	-	-	11.299%
2002-08-24T00:00:00	ANONYMOUS	v4_computers	2147483648	4290000000		-		-	-	0.334	-	-	11.336%
2002-10-19T00:00:00	ANONYMOUS	v4_computers	3221225472	4290000000		-		-	-	0.483	-	-	11.288%
2003-02-09T00:00:00	ANONYMOUS	v4_computers	4290000000	2147483647		-		-	-	0.632	-	-	11.236%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-09-22T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.073	-	-
1999-12-30T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.146	-	-
2000-02-23T00:00:00	ANONYMOUS	v4_computers	2⁵⁴	2⁵⁵		-	-	0.291	-	-
2000-08-01T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁶		-	-	1.166	-	-
2002-04-20T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁷		-	-	2.332	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1,402.547 GHz-days
Estimated T-Level:	42.714

Digits	B1	Curves	Complete	FacMiss
20	11000	7075 / 100	70.750	0.000%
25	50000	7075 / 280	25.268	0.000%
30	250000	7075 / 640	11.055	0.002%
35	1000000	7075 / 1580	4.478	1.134%
40	3000000	7075 / 4700	1.505	22.191%
45	11000000	5265 / 9700	0.543	58.111%

New Calculation Method

Total ECM effort:	1,402.547 GHz-days
Estimated T-Level:	42.714

Digits	B1	Complete	FacMiss
20	11000	2,117.000	0.000%
25	50000	830.030	0.000%
30	250000	204.222	0.000%
35	1000000	41.786	0.000%
40	3000000	7.188	0.076%
45	11000000	1.069	34.331%
50	44000000	0.141	86.882%
55	110000000	0.016	98.369%
60	260000000	0.002	99.829%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		1,810	11.52
11000000	30114149530	20866399143857514113654051017725144974702596369	465	103.9
11000000	36578884662		4,800	1,287

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13T13:12:00	Carsten Kossendey	durandal	3000000	300000000						1	0.006
2017-10-04T23:03:07	James Hintz	11_04_2016	3000000	300000000						1809	11.51
2021-03-20T13:08:11	Bruno Victal	Manual testing	11000000	30114149530	20866399143857514113654051017725144974702596369	153.870	465	2	1621620125413708	465	103.9
2021-05-23T11:45:15	Bruno Victal	Manual testing	11000000	36578884662						2400	643.5
2021-05-23T11:45:16	Bruno Victal	Manual testing	11000000	36578884662						2400	643.5

Lucas-Lehmer results:
Exponent "8233" not found

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:54:36

Oliver Kruse

Oliver-PC

195611422708913289323830429299939553967

BD94AA77A9CDCD__

2017-09-21T19:21:37

Oliver Kruse

Manual testing

195611422708913289323830429299939553967

BD94AA77A9CDCD__

2017-10-12T15:09:12

kkmrkkblmbrbk

Manual testing

195611422708913289323830429299939553967

BD94AA77A9CDCD__

2020-04-17T13:46:54

Oliver Kruse

Manual testing

195611422708913289323830429299939553967

EADECF918F4983__

2021-03-20T14:25:55

mikr

Nitron

195611422708913289323830429299939553967

20866399143857514113654051017725144974702596369

PRP

2021-03-21T14:28:28

Cork

3tits

195611422708913289323830429299939553967

20866399143857514113654051017725144974702596369

PRP

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 = 4290000000 (P-1 stage 1)

B1 = 3221225472, B2 = 4290000000 (P-1 stage 2)

B1 = 3221225472 (P-1 stage 1)

B1 = 3000000000, B2 = 4290000000 (P-1 stage 2)

B1 = 3000000000 (P-1 stage 1)

B1 = 2147483648, B2 = 4290000000 (P-1 stage 2)

B1 = 2147483648 (P-1 stage 1)

B1 = 43000000, B2 = 4290000000 (P-1 stage 2)

B1 = 43000000 (P-1 stage 1)

B1 = 1000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁷

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵³

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2⁸⁰

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2¹⁶⁰

Last modified: 2021-05-23T11:45:16+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