Weltrekordprimzahlen seit 1996

Status

August/September 2008: Neue Mersenne'sche Primzahlen!

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If in doubt, go to the real GIMPS Home Page

The page summarizes the current search status for Mersenne numbers with exponents below 79,300,000. The PrimeNet server also has a stats page updated every hour.

It can easily be proven that a Mersenne prime must have a prime number as an exponent. This table summarizes the current search status of Mersenne numbers with prime exponents.

Range		Mersenne		Composite			Status Unknown	Expected New Primes	P-90^* CPU Years	PII-400 Speed (sec.)	FFT Size (in K)
Low	High	Numbers	Primes	Factored	TwoLL	OneLL	Status Unknown	Expected New Primes	P-90^* CPU Years	PII-400 Speed (sec.)	FFT Size (in K)
0	2655500	193,635	35	124,229	69,371	0	0	0	0	N/A	Many
2655500	3290000	42,617	2	26,225	16,390	0	0	0	0	0.083	160
3290000	3935000	42,662	0	26,234	16,428	0	0	0	0	0.098	192
3935000	4598000	43,407	0	26,675	16,312	420	0	0.0001	0	0.119	224
4598000	5250000	42,364	0	26,262	15,298	804	0	0.0002	0	0.132	256
5250000	6515000	81,036	0	50,535	26,197	4,304	0	0.0008	0	0.173	320
6515000	7730000	77,076	1	47,369	3,662	26,037	7	0.0040	2	0.211	384
7730000	9020000	80,891	0	50,033	599	30,114	145	0.01	55	0.252	448
9020000	10320000	80,724	0	50,150	606	29,262	706	0.01	340	0.281	512
10320000	12830000	154,521	0	95,876	312	39,117	19,216	0.18	14,983	0.372	640
12830000	15270000	148,101	0	90,570	4	202	57,325	0.45	63,648	0.453	768
15270000	17850000	155,264	0	91,606	6	3	63,649	0.40	98,657	0.536	896
17850000	20400000	152,058	0	83,846	3	5	68,204	0.35	136,516	0.600	1024
Subtotal		1,294,356	38	789,610	165,188	130,268	209,252	1.40	314,201
20400000	25330000	290,867	0	155,669	2	0	135,196	0.56	418,692	0.776	1280
25330000	30100000	278,496	0	144,943	0	0	133,553	0.45	602,952	0.934	1536
30100000	35100000	288,751	0	152,397	2	109	136,243	0.40	861,279	1.113	1792
35100000	40250000	295,432	0	156,663	0	0	138,769	0.35	1,118,233	1.226	2048
40250000	49900000	547,607	0	286,434	0	0	261,173	0.55	3,359,095	1.64	2560
49900000	59400000	533,038	0	278,880	0	0	254,158	0.45	4,822,155	1.990	3072
59400000	69000000	534,127	0	274,490	0	0	259,637	0.39	6,918,687	2.380	3584
69000000	79300000	568,239	0	291,953	0	0	276,286	0.36	9,304,321	2.604	4096
Total		4,630,913	38	2,531,039	165,192	130,377	1,804,267	4.90	27,719,614

^*The time it would take one 90 MHz Pentium computer to run a first-time LL test on the remaining exponents. Further factoring will reduce this estimate. One PII-400 CPU year equals 5.5 P-90 CPU years.

All exponents below 4,069,400 have been tested and double-checked.
All exponents below 6,758,700 have been tested at least once.
Countdown to testing all exponents below M(6972593) at least once: 1
Countdown to proving M(6972593) is the 38th Mersenne Prime: 13,402

GIMPS Milestones

May 20, 2001: All exponents less than 4,000,000 double-checked.
April 6, 2001: First 10 million digit number sucessfully double-checked.
April 1, 2001: All exponents less than 6,000,000 tested at least once.
September 25, 2000: First 10 million digit number tested for primality.
May 19, 2000: Double-checking proves M(2976221) and M(3021377) are the 36th and 37th Mersenne primes.
March 15, 2000: All exponents less than 5,000,000 tested at least once.
October 16, 1999: All exponents less than 2,000,000 double-checked.
August 19, 1999: All exponents less than 4,000,000 tested at least once.
June 1, 1999: Prime M(6972593) is discovered!
December 26, 1998: All Mersenne numbers less than a million digits tested at least once.
December 18, 1998: Double-checking proves M(1398269) is the 35th Mersenne prime.
September 26, 1998: All exponents below M(3021377) tested at least once.
September 19, 1998: All exponents below M(2976221) tested at least once.
March 29, 1998: Double-checking proves M(1257787) is the 34th Mersenne prime.
March 5, 1998: All exponents below 2,000,000 tested at least once.
January 27, 1998: Prime M(3021377) is discovered!
October 30, 1997: All exponents below 1,000,000 double-checked.
October 11, 1997: All exponents below M(1398269) tested at least once.
August 30, 1997: Double-checking proves M(756839) and M(859433) are the 32nd and 33rd Mersenne primes.
August 28, 1997: All exponents below M(1257787) tested at least once.
August 24, 1997: Prime M(2976221) is discovered!
May 26, 1997: All exponents below 1,000,000 tested at least once.
March 28, 1997: All exponents below M(859433) tested at least once.
January 15, 1997: All exponents below M(756839) tested at least once.
November 13, 1996: Prime M(1398269) is discovered!
Third quarter, 1996: Double-checking proves M(216091) is the 31st Mersenne prime.

The Mersenne Database

The database is available in human-readable form. There are European, and Canadian mirror sites. You will need a special program to decompress the known factors data and the how far factored data. UNIX users can unzip files with a free program from PKWare.

A 6.3MB zip file of smallest known factors of Mersenne numbers.
A 4.0MB zip file of double-checked exponents and their residues.
A 0.9MB zip file of exponents that have not been verified.
A 0.8MB zip file of exponents and how far they have been trial factored.
A 0.2MB zip file of exponents and how much P-1 factoring has been done.
A 0.7MB zip file of user IDs and associated user names.
A small file of programs used in LL testing.
A 0.2MB list of exponents below 12,000,000 that have not been tested.

Diese Seite wurde das letzte Mal am 25. July 2001 geändert (Originalseite am 22. Juli 2001).