M28499 Mersenne number exponent details

is 2 ²⁸⁴⁹⁹ - 1

has 8580 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	Prob over default TF
Actual	2⁶⁷	1,042.6302	77.6119%	500000000	10000000000	0.8128	13.6524%	1,043.4429	80.6684%	3.0565%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.0501%	0.0000	64.0188%	1.5188%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7322%	0.0001	66.4996%	0.5905%
Difference	+23	+1,042.6301	+11.7028%	+499999500	+9999990000	+0.8128	+11.9201%	+1,043.4429	+14.1688%	+14.1688%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
28499	56999	5	15.799	1 1	-	1	1	1.532e-13	7.987e-10	1.626e-9
28499	227993	6	17.799	4 2²	2008-08-26	4	4	6.132e-13	3.195e-9	6.502e-9
28499	3647873	7	21.799	64 2⁶	2008-08-26	64	64	9.939e-12	5.112e-8	1.040e-7
28499	1048551795486348681767	22	69.829	18396291018743617 7 × 47 × 222773 × 250998901	2009-04-04	222773	250998901	5,149.0	0.0111	0.0204
28499	10676316734584051356525414741806399	35	113.040	187310374654971250860125175301 445507 × 420443168468668844395543	2018-02-09	445507	420443168468668844395543	5.705e+12	1.830e+13	3.417e+13

exponent	prime factors	composite factor	digits	bits*
28499	56999 227993	12995373007	11	33.597
28499	56999 3647873	207925113127	12	37.597
28499	227993 3647873	831689508889	12	39.597
28499	56999 227993 3647873	47405470317164111	17	55.396
28499	56999 1048551795486348681767	59766403790926388512037233	26	85.628
28499	227993 1048551795486348681767	239062469508319095002103631	27	87.628
28499	3647873 1048551795486348681767	3824983783856173224803431591	28	91.628
28499	56999 227993 1048551795486348681767	13626321699504680096024904863369	32	103.426
28499	56999 3647873 1048551795486348681767	218020250696018017640570797255409	33	107.426
28499	227993 3647873 1048551795486348681767	872069527832720502042608778726863	33	109.426
28499	56999 227993 3647873 1048551795486348681767	49707091016937235895926657778652464137	38	125.225
28499	56999 10676316734584051356525414741806399	608539377554556343270592114868222936601	39	128.839
28499	227993 10676316734584051356525414741806399	2434125481268021620928298883228666327207	40	130.839
28499	3647873 10676316734584051356525414741806399	38945847555537327174082434250437534139327	41	134.839
28499	56999 227993 10676316734584051356525414741806399	138742718306795964371292108045150751984471793	45	146.637
28499	56999 3647873 10676316734584051356525414741806399	2219874364818072111595524669840689008407499673	46	150.637
28499	227993 3647873 10676316734584051356525414741806399	8879380621729621834400576432060004721027580711	46	152.637
28499	56999 227993 3647873 10676316734584051356525414741806399	50611581605796671493899845605098820909385107294628 9	51	168.436
28499	1048551795486348681767 10676316734584051356525414741806399	11194671081229058198248823986948924807046695817975 227033	56	182.869
28499	56999 1048551795486348681767 10676316734584051356525414741806399	63808505695897508824198471843210176507685461492876 9965653967	60	198.668
28499	227993 1048551795486348681767 10676316734584051356525414741806399	25523066438226566657933441272564462135329973196276 25936934769	61	200.667
28499	3647873 1048551795486348681767 10676316734584051356525414741806399	40836738381096288216820532303743335182655851413604 745362550809	62	204.667
28499	56999 227993 1048551795486348681767 10676316734584051356525414741806399	14547892639124760729355482190949017772516731422145 5050779344898231	66	216.466
28499	56999 3647873 1048551795486348681767 10676316734584051356525414741806399	23276532509841073320705535207810663620762008747240 56880920033562191	67	220.466
28499	227993 3647873 1048551795486348681767 10676316734584051356525414741806399	93104904937212860394175636215273542182992555313419 86709444046596337	67	222.466
28499	56999 227993 3647873 1048551795486348681767 10676316734584051356525414741806399	53068864765161958296076170886343766308883926603096 1900451601211944612663	72	238.265

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-12-28T07:28:38	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 56999 skipped known factor: 227993 skipped known factor: 3647873 skipped known factor: 1048551795486348681767	-	-	0.813	-	-	13.652%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	227993	17.799	6	5.30471e-16	3.73488e-5	1.26209e-15
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	3647873	21.799	7	1.35801e-13	3.73488e-5	3.23094e-13

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.200 GHz-days
Estimated T-Level:	31.617

Digits	B1	Curves	Complete	FacMiss
20	11000	1270 / 100	12.700	0.000%
25	50000	1270 / 280	4.536	1.063%
30	250000	1119 / 640	1.748	17.381%
35	1000000	511 / 1580	0.323	72.360%
40	3000000	500 / 4700	0.106	89.907%

New Calculation Method

Total ECM effort:	19.200 GHz-days
Estimated T-Level:	31.617

Digits	B1	Complete	FacMiss
20	11000	157.109	0.000%
25	50000	31.889	0.000%
30	250000	5.496	0.410%
35	1000000	0.797	45.086%
40	3000000	0.098	90.623%
45	11000000	0.011	98.945%
50	44000000	0.001	99.899%

ECM Summary

B1	B2	factor	curves	GHz-days
		1048551795486348681767	1	0.00000e+0
50000	5000000		151	0.087
250000	25000000		608	1.747
1000000	100000000		11	0.126
3000000	300000000		40	1.379
3000000	300000000	10676316734584051356525414741806399	460	15.86

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-04T14:31:00	Matthias Wurtinger	WUR_E6600	50000	5000000						17	0.010
2009-04-04T14:31:00	Matthias Wurtinger	WUR_E6600			1048551795486348681767	69.829		1		1	-
2009-05-10T17:33:00	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.086
2010-04-18T21:28:00	James Hintz	10_122109	50000	5000000						3	0.002
2010-04-19T13:43:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20T08:56:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T04:28:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21T23:46:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-22T19:16:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-23T16:51:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-24T09:06:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-25T02:06:00	James Hintz	14_091909	50000	5000000						32	0.018
2010-04-25T04:32:00	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-26T00:31:00	James Hintz	10_122109	50000	5000000						11	0.006
2011-03-20T00:44:00	James Hintz	17_051310	250000	25000000						11	0.032
2014-11-19T02:48:00	James Hintz	08_04_2014	250000	25000000						567	1.629
2014-11-19T03:14:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2018-02-09T18:39:33	nordi	nordiputer	3000000	300000000	10676316734584051356525414741806399	113.040	460	2		460	15.86
2018-02-09T23:33:50	nordi	nordiputer	3000000	300000000						40	1.379

Lucas-Lehmer results:
No L-L results for M28499

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:38:22

Oliver Kruse

Ollaptop

56999

227993

3647873

1048551795486348681767

6A022E709D906509

2017-09-21T21:28:58

Oliver Kruse

Manual testing

56999

227993

3647873

1048551795486348681767

6A022E709D906509

2017-10-02T10:29:34

kkmrkkblmbrbk

Manual testing

56999

227993

3647873

1048551795486348681767

6A022E709D9065__

2017-12-07T03:12:08

ATH

xps

56999

227993

3647873

1048551795486348681767

6A022E709D9065__

2018-02-09T23:42:01

ANONYMOUS

dory

56999

227993

3647873

1048551795486348681767

10676316734584051356525414741806399

581E765A716E1D__

2018-02-10T16:51:10

Daniel Bamberger

Backup_laptop

56999

227993

3647873

1048551795486348681767

10676316734584051356525414741806399

581E765A716E1D__

2022-05-12T18:18:47

Jorge Coveiro

Manual testing

56999

581E765A716E1D1C

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

TF factor-bounds graph:

2⁶⁷

2¹⁰

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2022-05-12T18:18:47+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