M8 273 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	400000000	400000000	0.0590	29.9191%	0.0590	29.9191%
Target	2⁴⁴	0.0003	68.1818%	500	10000	0.0000	1.1921%	0.0003	68.5611%
Difference	-44	-0.0003	-68.1818%	+399999500	+399990000	+0.0590	+28.7270%	+0.0587	-38.6420%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8273	1042399	7	19.991	63 3² × 7	-	9	9	8.558e-12	1.327e-9	2.700e-9
8273	28062017	8	24.742	1696 2⁵ × 53	-	32	53	3.693e-10	4.886e-9	9.601e-9
8273	62014409	8	25.886	3748 2² × 937	-	4	937	9.787e-10	8.083e-9	1.408e-8
8273	58965335525351	14	45.745	3563721475 5² × 17 × 613 × 13679	-	613	13679	0.0007	1.953e-7	2.052e-7
8273	5967764427340016644604473	25	82.303	360677168339176637532 2² × 3³ × 619 × 5395158983114591	-	619	5395158983114591	220,180,580	43,332	80,932

exponent	prime factors	composite factor	digits	bits*
8273	1042399 28062017	29251818458783	14	44.734
8273	1042399 62014409	64643757927191	14	45.878
8273	28062017 62014409	1740249399602953	16	50.628
8273	1042399 58965335525351	61465406786290357049	20	65.736
8273	28062017 58965335525351	1654686247923103692967	22	70.487
8273	1042399 28062017 62014409	1814034233896718604247	22	70.620
8273	62014409 58965335525351	3656700434091346782559	22	71.631
8273	1042399 28062017 58965335525351	1724843290148795366445107833	28	90.479
8273	1042399 62014409 58965335525351	3811740875796385794792719041	28	91.623
8273	28062017 62014409 58965335525351	102614389745378752965065961503	30	96.373
8273	1042399 5967764427340016644604473	6220791671294806010319058050727	31	102.295
8273	28062017 5967764427340016644604473	167467506812010811861173679602041	33	107.046
8273	62014409 5967764427340016644604473	370087384012714574265309431851457	33	108.190
8273	1042399 28062017 62014409 58965335525351	106965137256193066712031793204765697	36	116.365
8273	1042399 28062017 5967764427340016644604473	174567961633333258273275582443487936359	39	127.037
8273	58965335525351 5967764427340016644604473	351891231794358250022183777203059495023	39	128.048
8273	1042399 62014409 5967764427340016644604473	385778719007469659499584286452526925343	39	128.181
8273	28062017 62014409 5967764427340016644604473	10385398461650324599180875786875927808769	41	132.932
8273	1042399 58965335525351 5967764427340016644604473	366811068131207245464874347172692014552480177	45	148.040
8273	28062017 58965335525351 5967764427340016644604473	9874777728764221716212771532996468001346841391	46	152.791
8273	1042399 28062017 62014409 5967764427340016644604473	10825728971025836711861545739363680271932996831	47	152.923
8273	62014409 58965335525351 5967764427340016644604473	21822326772009136409399963832635407575689786407	47	153.934
8273	1042399 28062017 58965335525351 5967764427340016644604473	10293458429686095952758476833223985248135946119137 009	53	172.782
8273	1042399 62014409 58965335525351 5967764427340016644604473	22747571604815551784022112899175316221491457660870 393	53	173.926
8273	28062017 62014409 58965335525351 5967764427340016644604473	61237850485567551007590074487079996219093557287960 2919	54	178.677
8273	1042399 28062017 62014409 58965335525351 5967764427340016644604473	63834274108305129602760886055257700978786905023412 5203162681	60	198.668

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-27	Seth_Tr	Manual testing	100000000	100000000		-	skipped known factor: 1042399 skipped known factor: 28062017 skipped known factor: 62014409 skipped known factor: 58965335525351	-	-	0.015	-	-	26.233%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 1042399 skipped known factor: 28062017 skipped known factor: 62014409 skipped known factor: 58965335525351	-	-	0.059	-	-	29.919%

ECM factoring results:

Total ECM effort:	1,312.037 GHz-days
Estimated T-Level:	45.778

Digits	B1	Complete	FacMiss
20	11000	3,184.200	0.000%
25	50000	892.083	0.000%
30	250000	233.274	0.000%
35	1000000	47.257	0.000%
40	3000000	8.057	0.032%
45	11000000	1.194	30.306%
50	44000000	0.156	85.583%
55	110000000	0.018	98.189%
60	260000000	0.002	99.813%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		3,921	24.95
11000000	36578884662		4,800	1,287

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.006
2013-04-18	Axon		3000000	300000000						30	0.191
2017-11-20	James Hintz	10_12_2017	3000000	300000000						2000	12.73
2017-12-09	James Hintz	10_12_2017	3000000	300000000						1000	6.364
2017-12-12	James Hintz	10_12_2017	3000000	300000000						887	5.645
2017-12-12	James Hintz	10_12_2017	3000000	300000000						3	0.019
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	643.5
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	643.5

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-25

Oliver Kruse

Doppelherz

1042399

28062017

62014409

58965335525351

5967764427340016644604473

210D6EF53CDF8CDB

2017-09-27

Oliver Kruse

Manual testing

1042399

28062017

62014409

58965335525351

5967764427340016644604473

210D6EF53CDF8C__

2017-10-09

Chang Chia-Tche

homura

210D6EF53CDF8C__

2017-10-12

kkmrkkblmbrbk

Manual testing

1042399

28062017

62014409

58965335525351

5967764427340016644604473

210D6EF53CDF8C__

2020-04-17

Oliver Kruse

Manual testing

1042399

28062017

62014409

58965335525351

5967764427340016644604473

26798C300DEE0A__

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 = 400000000 (P-1 stage 1)

B1 = 100000000 (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

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