M8 563 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	0.0707	29.9725%	0.0707	29.9725%
Target	2⁴⁴	0.0003	68.1818%	500	10000	0.0000	1.2048%	0.0003	68.5652%
Difference	-44	-0.0003	-68.1818%	+399999500	+399990000	+0.0707	+28.7677%	+0.0705	-38.5927%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8563	32402393	8	24.950	1892 2² × 11 × 43	-	11	43	3.679e-10	2.253e-9	3.958e-9
8563	240780682609487	15	47.775	14059364861 20477 × 686593	-	20477	686593	0.0034	1.004e-5	1.235e-5
8563	206858361127703737	18	57.521	12078615037236 2² × 3 × 11 × 23 × 50683 × 78497	-	50683	78497	2.7545	9.230e-6	1.824e-5
8563	235035115803166906361	21	67.671	13723876900803860 2² × 5 × 7 × 7333 × 13368020203	-	7333	13368020203	3,893.2	0.1288	0.2405
8563	9139671749156544671917417	25	82.918	533672296458983105916 2² × 3 × 338339 × 131444176910087	-	338339	131444176910087	149,441,438	1,266.3	2,365.1
8563	316515574095503525384055959	27	88.032	18481582044581544165833 18481582044581544165833	-	1	18481582044581544165833	1.320e+10	1.780e+11	3.325e+11

exponent	prime factors	composite factor	digits	bits*
8563	32402393 240780682609487	7801870304720863302391	22	72.724
8563	32402393 206858361127703737	6702705912595779673842641	25	82.471
8563	32402393 235035115803166906361	7615700191054724744503321873	28	92.621
8563	240780682609487 206858361127703737	49807497395808276837449401552919	32	105.296
8563	32402393 9139671749156544671917417	296147235907167778981524209178881	33	107.868
8563	32402393 316515574095503525384055959	10255862022463124762379657117509887	35	112.982
8563	240780682609487 235035115803166906361	56591915620286353098956506459246807	35	115.446
8563	206858361127703737 235035115803166906361	48618978862503167473569104698028771057	38	125.193
8563	32402393 240780682609487 206858361127703737	1613882104965456338739832626732491735167	40	130.246
8563	240780682609487 9139671749156544671917417	2200656402588556866245916855391324735079	40	130.693
8563	240780682609487 316515574095503525384055959	76210835987248999684123462909936152283033	41	135.807
8563	32402393 240780682609487 235035115803166906361	1833713490551357185649156612199553524409151	43	140.396
8563	206858361127703737 9139671749156544671917417	1890617519275696200576736960584830106287329	43	140.440
8563	206858361127703737 316515574095503525384055959	65473892928790138361363906299241505181418783	44	145.554
8563	32402393 206858361127703737 235035115803166906361	1575371260361520596223403243083674565095939401	46	150.142
8563	235035115803166906361 9139671749156544671917417	2148143807965941513891838970338164525963989537	46	150.590
8563	32402393 240780682609487 9139671749156544671917417	71306533614640636882948632593713872856650644047	47	155.643
8563	235035115803166906361 316515574095503525384055959	74392274611042526532908448733281743984537055199	47	155.704
8563	32402393 240780682609487 316515574095503525384055959	2469413458517385076621844305728674811182682497969	49	160.757
8563	32402393 206858361127703737 9139671749156544671917417	61260531872256183639694257654495174942153805178297	50	165.389
8563	32402393 206858361127703737 316515574095503525384055959	21215108099185790777092893079231988527998677043477 19	52	170.503
8563	9139671749156544671917417 316515574095503525384055959	28928484507287386255860941139079640374945089547379 03	52	170.951
8563	240780682609487 206858361127703737 235035115803166906361	11706510918289732461416654037283984465813782459217 759	53	172.968
8563	32402393 235035115803166906361 9139671749156544671917417	69604999886228967548138325809612549868943892825762 041	53	175.539
8563	32402393 235035115803166906361 316515574095503525384055959	24104877181109220844322269888761472483123555856206 91207	55	180.653
8563	240780682609487 206858361127703737 9139671749156544671917417	45522417684465707717046176890513619174196191156912 3290223	57	188.215
8563	240780682609487 206858361127703737 316515574095503525384055959	15764848632494553529013078868368068858894355566857 395794321	59	193.329
8563	32402393 9139671749156544671917417 316515574095503525384055959	93735212389953725340520476813832616572763814493436 745001879	59	195.900
8563	32402393 240780682609487 206858361127703737 235035115803166906361	37931896743321479907967976086111231726719324406008 0299697287	60	197.917
8563	240780682609487 235035115803166906361 9139671749156544671917417	51723153242538215557272725698959628370431299059593 8324937519	60	198.365
8563	240780682609487 235035115803166906361 316515574095503525384055959	17912222661719228545457268098524386107847919900990 401880072913	62	203.479
8563	206858361127703737 235035115803166906361 9139671749156544671917417	44436150758245939727618564072750557990366858433140 3848303799769	63	208.111
8563	32402393 240780682609487 206858361127703737 9139671749156544671917417	14750352681222078564708630227539402603346404449693 979515258703639	65	213.164
8563	206858361127703737 235035115803166906361 316515574095503525384055959	15388664006602341011656806372193250093975939562934 321002887578663	65	213.225
8563	32402393 240780682609487 206858361127703737 316515574095503525384055959	51081882097560109380661868363285743581695645455905 1113484136210153	66	218.278
8563	240780682609487 9139671749156544671917417 316515574095503525384055959	69654202465226260695766910915553700938282471469731 5194886186285761	66	218.726
8563	32402393 240780682609487 235035115803166906361 9139671749156544671917417	16759539385639475780054648662788895695926645316294 897808387191082967	68	223.314
8563	32402393 240780682609487 235035115803166906361 316515574095503525384055959	58039887818853249898672476563474987875022868486441 2090946061395680809	69	228.428
8563	206858361127703737 9139671749156544671917417 316515574095503525384055959	59840988950856368541885238857833677922280735052656 2709656977068643511	69	228.472
8563	32402393 206858361127703737 235035115803166906361 9139671749156544671917417	14398376202759329297086096671809441709731571611259 789734452103508447217	71	233.061
8563	32402393 206858361127703737 235035115803166906361 316515574095503525384055959	49862953888688364817972142119670996149229532626244 6102323717458656940559	72	238.175
8563	235035115803166906361 9139671749156544671917417 316515574095503525384055959	67992097061804105741258231037093171689723724391986 0593165498326098500983	72	238.622
8563	32402393 240780682609487 9139671749156544671917417 316515574095503525384055959	22569628423798301329846928838817608304066973855735 282989573798302438226073	74	243.675
8563	32402393 206858361127703737 9139671749156544671917417 316515574095503525384055959	19389912414943057400470024703703979606731638335050 441857450266170175020321823	77	253.422
8563	240780682609487 206858361127703737 235035115803166906361 9139671749156544671917417	10699366712108530708537935160064632729809600941603 7187070407788862400467808503	78	255.886
8563	240780682609487 206858361127703737 235035115803166906361 316515574095503525384055959	37052930239577548309753368044103085387930382395812 21208676345664892729822575881	79	261.000
8563	32402393 235035115803166906361 9139671749156544671917417 316515574095503525384055959	22031066498907219232418055165486905267069021791728 183444961590803085785562052319	80	263.572
8563	240780682609487 206858361127703737 9139671749156544671917417 316515574095503525384055959	14408554167613965734249068871410102588439573237257 0011997358050867047376090829588857	84	276.247
8563	32402393 240780682609487 206858361127703737 235035115803166906361 9139671749156544671917417	34668508505685847067061463046493213511195350488301 37438069871844980522881314962947679	85	280.836
8563	32402393 240780682609487 206858361127703737 235035115803166906361 316515574095503525384055959	12006036074243758743091143644386695052522777070293 8885023465962037700534553923968483233	87	285.950
8563	240780682609487 235035115803166906361 9139671749156544671917417 316515574095503525384055959	16371183542591687992688071403147116637099576684337 0823052297299174515544143207474625721	87	286.397
8563	206858361127703737 235035115803166906361 9139671749156544671917417 316515574095503525384055959	14064733767840557897966472015194254885474033812502 2818674849511751250233610292068627273471	90	296.144
8563	32402393 240780682609487 206858361127703737 9139671749156544671917417 316515574095503525384055959	46687163470081559000967188945549660824093630878588 35948753110525908059829713864034172934801	91	301.197
8563	32402393 240780682609487 235035115803166906361 9139671749156544671917417 316515574095503525384055959	53046552302218811287246001601683431009213886385952 70853273996640691228245937056873360139750353	94	311.347
8563	32402393 206858361127703737 235035115803166906361 9139671749156544671917417 316515574095503525384055959	45573103098594051834916352705982621814129963488798 72504670213095622128310782492452443885525816103	97	321.093
8563	240780682609487 206858361127703737 235035115803166906361 9139671749156544671917417 316515574095503525384055959	33865161973413515878926916565102781829309705820482 72000889838437251104997007969763570179217931824801 9377	104	343.918
8563	32402393 240780682609487 206858361127703737 235035115803166906361 9139671749156544671917417 316515574095503525384055959	10973122872712002930207303688206704222265520067096 68543437288947503161437973160604113180300998596344 395325169161	112	368.868

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: 32402393 skipped known factor: 240780682609487 skipped known factor: 206858361127703737	-	-	0.018	-	-	26.287%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 32402393 skipped known factor: 240780682609487 skipped known factor: 206858361127703737	-	-	0.071	-	-	29.972%

ECM factoring results:

Total ECM effort:	1,574.608 GHz-days
Estimated T-Level:	45.778

Digits	B1	Complete	FacMiss
20	11000	3,192.200	0.000%
25	50000	887.222	0.000%
30	250000	232.442	0.000%
35	1000000	47.128	0.000%
40	3000000	8.045	0.032%
45	11000000	1.192	30.350%
50	44000000	0.156	85.591%
55	110000000	0.018	98.190%
60	260000000	0.002	99.813%

ECM Summary

B1	B2	curves	GHz-days
3000000	300000000	2,711	20.69
3000000	600000000	1,000	10.12
11000000	36578884662	4,800	1,544

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.008
2013-04-18	Axon		3000000	300000000						30	0.229
2017-01-25	Ismo Laitela	6600K	3000000	600000000						1000	10.12
2017-12-03	James Hintz	10_12_2017	3000000	300000000						1000	7.633
2018-03-15	James Hintz	3_1_2018	3000000	300000000						1680	12.82
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

A72AD74C52EC52__

2017-09-21

Oliver Kruse

Manual testing

A72AD74C52EC52__

2017-10-02

kkmrkkblmbrbk

Manual testing

32402393

240780682609487

206858361127703737

235035115803166906361

9139671749156544671917417

316515574095503525384055959

A72AD74C52EC52__

2017-12-07

ATH

Manual testing

32402393

240780682609487

206858361127703737

235035115803166906361

9139671749156544671917417

316515574095503525384055959

A72AD74C52EC52__

2020-04-17

Oliver Kruse

Manual testing

32402393

240780682609487

206858361127703737

235035115803166906361

9139671749156544671917417

316515574095503525384055959

B59DCEB21333CD__

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

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

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