M8 221 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	10000000	1000000000	0.0094	33.9785%	0.0094	33.9785%
Target	2⁴⁴	0.0003	68.1818%	500	10000	0.0000	1.1897%	0.0003	68.5604%
Difference	-44	-0.0003	-68.1818%	+9999500	+999990000	+0.0094	+32.7887%	+0.0091	-34.5819%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8221	920753	6	19.812	56 2³ × 7	-	8	8	8.599e-12	1.179e-9	2.400e-9
8221	9667897	7	23.205	588 2² × 3 × 7²	-	49	49	1.532e-10	7.223e-9	1.470e-8
8221	18480809	8	24.140	1124 2² × 281	-	4	281	3.380e-10	2.814e-9	4.208e-9
8221	66413573927432647	17	55.882	4039263710463 3 × 1346421236821	-	3	1346421236821	0.8344	10.814	20.198
8221	50435132990814087944946096143	29	95.348	3067457303905491299412851 47 × 691 × 2993681 × 3095621 × 10191763	-	3095621	10191763	1.840e+12	0.0005	0.0009

exponent	prime factors	composite factor	digits	bits*
8221	920753 9667897	8901745166441	13	43.017
8221	920753 18480809	17016260329177	14	43.952
8221	9667897 18480809	178670557888673	15	47.344
8221	920753 9667897 18480809	164511452187669330769	21	67.157
8221	920753 66413573927432647	61150497434405392023191	23	75.695
8221	9667897 66413573927432647	642079592132304305633359	24	79.087
8221	18480809 66413573927432647	1227376574760262609571423	25	80.022
8221	920753 9667897 66413573927432647	591196710694595586324832199327	30	98.900
8221	920753 18480809 66413573927432647	1130110663340236078550716441519	31	99.834
8221	9667897 18480809 66413573927432647	11866150304995018602287731707431	32	103.227
8221	920753 50435132990814087944946096143	46438300006691043917572952861955679	35	115.161
8221	9667897 50435132990814087944946096143	487601670936492548400680528062621271	36	118.553
8221	18480809 50435132990814087944946096143	932082059692833913819751318114419687	36	119.488
8221	920753 9667897 18480809 66413573927432647	10925793491775078363112235832812215543	38	123.039
8221	920753 9667897 50435132990814087944946096143	448960701319788323417571798255242723137063	42	138.366
8221	920753 18480809 50435132990814087944946096143	858217352708355904651277485407806270064311	42	139.300
8221	9667897 18480809 50435132990814087944946096143	9011273348658169916916232309144443748688239	43	142.693
8221	66413573927432647 50435132990814087944946096143	3349577433425328650627833804930297157218980521	46	151.231
8221	920753 9667897 18480809 50435132990814087944946096143	8297156969597055925510371647341674014935942123967	49	162.505
8221	920753 66413573927432647 50435132990814087944946096143	30841334705586716310515298593909858984008479716523 13	52	171.043
8221	9667897 66413573927432647 50435132990814087944946096143	32383369619880434585418882559184205095385910122034 337	53	174.436
8221	18480809 66413573927432647 50435132990814087944946096143	61902900777843714554480726632660080075806950183321 489	53	175.370
8221	920753 9667897 66413573927432647 50435132990814087944946096143	29817084727613769785828192373016534394191862902593 481895761	59	194.248
8221	920753 18480809 66413573927432647 50435132990814087944946096143	56997281599901933707181792489201666710039476802143 810961217	59	195.183
8221	9667897 18480809 66413573927432647 50435132990814087944946096143	59847086872141291441012055356971449018465378625648 3273538633	60	198.575
8221	920753 9667897 18480809 66413573927432647 50435132990814087944946096143	55104384778784710518186173006097532598099052765701 5743560516950649	66	218.387

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-25	H Michaelson		10000000	1000000000		-	skipped known factor: 920753 skipped known factor: 9667897 skipped known factor: 18480809 skipped known factor: 50435132990814087944946096143	-	-	0.009	-	-	33.978%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 920753 skipped known factor: 9667897 skipped known factor: 18480809 skipped known factor: 50435132990814087944946096143	-	-	0.059	-	-	29.909%

ECM factoring results:

Total ECM effort:	1,311.834 GHz-days
Estimated T-Level:	45.778

Digits	B1	Complete	FacMiss
20	11000	3,177.800	0.000%
25	50000	890.398	0.000%
30	250000	232.937	0.000%
35	1000000	47.203	0.000%
40	3000000	8.050	0.032%
45	11000000	1.193	30.330%
50	44000000	0.156	85.589%
55	110000000	0.018	98.190%
60	260000000	0.002	99.813%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		3,889	24.75
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
2017-09-27	James Hintz	11_04_2016	3000000	300000000						3858	24.55
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

2017-09-21

Oliver Kruse

Oliver-PC

E3FBBDFA850BC9__

2017-09-21

Oliver Kruse

Manual testing

E3FBBDFA850BC9__

2017-10-02

kkmrkkblmbrbk

Manual testing

920753

9667897

18480809

66413573927432647

50435132990814087944946096143

E3FBBDFA850BC9__

2017-12-07

ATH

Manual testing

920753

9667897

18480809

66413573927432647

50435132990814087944946096143

E3FBBDFA850BC9__

2020-04-17

Oliver Kruse

Manual testing

920753

9667897

18480809

66413573927432647

50435132990814087944946096143

859897F075C263__

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 = 10000000, B2 = 1000000000 (P-1 stage 2)

B1 = 10000000 (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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=45.78 ~= 135-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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