M1672637 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	17.7647	68.6567%	500000	15000000	0.0880	5.0139%	17.8527	70.2282%	1.5715%
PrimeNet	2⁵⁷	0.0115	63.1579%	7000	120000	0.0009	2.5703%	0.0124	64.1048%	0.9469%
GPU72	2⁶¹	0.1837	65.5738%	7000	80000	0.0007	1.2072%	0.1844	65.9894%	0.4156%
Difference	+6	+17.5811	+3.0829%	+493000	+14920000	+0.0873	+3.8067%	+17.6683	+4.2389%	+4.2389%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1672637	13381097	8	23.674	4 2²	-	4	4	6.687e-13	2.730e-7	5.555e-7
1672637	718146695951	12	39.385	214675 5² × 31 × 277	2008-07-15	31	277	6.421e-8	3.030e-6	4.305e-6
1672637	11071050492041	14	43.332	3309460 2² × 5 × 7² × 11 × 307	2008-09-30	49	307	9.341e-7	4.303e-6	6.805e-6
1672637	6292358170451872327	19	62.448	1880969442399 3² × 317 × 10861 × 60703	2015-04-29	10861	60703	0.9210	0.0009	0.0015
1672637	254181561033970325423	21	67.784	75982284570403 1498531 × 50704513	2018-02-03	1498531	50704513	29.303	0.2852	0.3521

exponent	prime factors	composite factor	digits	bits*
1672637	13381097 718146695951	9609590598749838247	19	63.059
1672637	13381097 11071050492041	148142800525898348977	21	67.006
1672637	718146695951 11071050492041	7950638331565936972425991	25	82.717
1672637	13381097 6292358170451872327	84198655037559037439202719	26	86.122
1672637	13381097 254181561033970325423	3401228123806977219606729031	28	91.458
1672637	718146695951 6292358170451872327	4518836229850291388296739847977	31	101.834
1672637	11071050492041 6292358170451872327	69663015019079407673143061649407	32	105.780
1672637	13381097 718146695951 11071050492041	106388262726601964523918510892127	33	106.391
1672637	718146695951 254181561033970325423	182539648228213236473907706462273	33	107.170
1672637	11071050492041 254181561033970325423	2814056896352886643990097041458343	34	111.116
1672637	13381097 718146695951 6292358170451872327	60466985918741044545063340689545490769	38	125.507
1672637	13381097 11071050492041 6292358170451872327	932167561282758404776871602807695059479	39	129.454
1672637	6292358170451872327 254181561033970325423	1599401422350314438177885452907838269321	40	130.233
1672637	13381097 718146695951 254181561033970325423	2442580739287599453941296989219201853481	40	130.844
1672637	13381097 11071050492041 254181561033970325423	37655168293616922413235955551167109142271	41	134.790
1672637	718146695951 11071050492041 6292358170451872327	50028264065936765846169846682861937388451057	44	145.166
1672637	718146695951 11071050492041 254181561033970325423	2020905662333951205522725001487169292053269193	46	150.502
1672637	13381097 6292358170451872327 254181561033970325423	21401745574407525477758788500248715942096425137	47	153.906
1672637	13381097 718146695951 11071050492041 6292358170451872327	66943305420791425965388579693850382180279027346952 9	51	168.839
1672637	718146695951 6292358170451872327 254181561033970325423	11486048469602081986433792908015112584227502382192 71	52	169.618
1672637	11071050492041 6292358170451872327 254181561033970325423	17707053903882523915460345218900259005791906924974 161	53	173.565
1672637	13381097 718146695951 11071050492041 254181561033970325423	27041934695539847474366518949224956552386124238644 721	53	174.175
1672637	13381097 718146695951 6292358170451872327 254181561033970325423	15369592871844701046242326698006229895546887944385 172520287	59	193.292
1672637	13381097 11071050492041 6292358170451872327 254181561033970325423	23693980587208072911759467902759059908162506837805 0970834617	60	197.238
1672637	718146695951 11071050492041 6292358170451872327 254181561033970325423	12716262256099490480738586566115060842827590130425 910168198322111	65	212.950
1672637	13381097 718146695951 11071050492041 6292358170451872327 254181561033970325423	17015753872630612377333965848408254229877773781147 1755273948063404535767	72	236.624

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-04-30T11:21:00	alpertron	Manual testing	500000	15000000	12		6292358170451872327	19	62.448	0.034	0.157	0.068	5.014%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-09-30T13:30:00	markr	Manual testing	?	?	11071050492041	43.332	14	2.33523e-7	0.171	5.08759e-7
2008-07-15T07:45:00	J Feitsma	Manual testing	?	?	718146695951	39.385	12	2.04238e-8	0.171	4.44961e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.894 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.894 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	14.72
50000	5000000	254181561033970325423	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-08-27T23:52:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-02-03T19:20:14	Chang Chia-Tche	exbpc13	50000	5000000	254181561033970325423	67.784	3	2		3	0.178
2019-03-19T04:59:34	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-12-16T13:28:38	TJAOI	Manual testing	50000	5000000						244	14.48

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T22:57:26

Oliver Kruse

GTX-0

13381097

718146695951

11071050492041

6292358170451872327

E495F7EC79D131C3

2017-10-03T00:14:32

kkmrkkblmbrbk

Manual testing

13381097

718146695951

11071050492041

6292358170451872327

E495F7EC79D131__

2017-11-14T07:44:54

ATH

ec2-1xf

13381097

718146695951

11071050492041

6292358170451872327

E495F7EC79D131__

2018-02-04T19:54:06

-p95holder- @bopoh13

Lucius_Yorkfield

13381097

718146695951

11071050492041

6292358170451872327

254181561033970325423

240CB25E4BE980__

2018-02-05T04:09:49

AdolfNor

Manual testing

13381097

718146695951

11071050492041

6292358170451872327

254181561033970325423

240CB25E4BE980__

2018-02-05T07:00:58

-p95holder- @bopoh13

t_i3-2100

13381097

718146695951

11071050492041

6292358170451872327

254181561033970325423

240CB25E4BE980__

2018-02-15T04:23:15

trebor

Desktop

13381097

718146695951

11071050492041

6292358170451872327

254181561033970325423

240CB25E4BE980__

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