prime10
For the background of the search see the home page of Tony Forbes.
Newsletter1.
On March the second 1998 at 11.56 AM, Manfred Toplic (our lucky man) found 10 consecutive primes in arithmetic progression with N=507618446770482 !! The first prime is :
1009969724697142476377866555879698403295093246\ 89190041803603417758904341703348882159067229719.
The primality of the ten numbers p, p+210, …, p+1890 was checked independently by François Morain using his ECPP program. The prime certificates are available from ftp://lix.polytechnique.fr/pub/submissions/morain/Certif/AP/10, files p10-1.certif to p10-10.certif.
News
Ranges of 10^12 values which are finished: 303, 305, 500-502, 504-505, 508, 512, 514, 516, 518, 520, 522, 530, 532, 536, 538, 542, 546, 548, 566.
10 primes in AP found (not necessarily consecutive)
Remark : The expected number of such “near misses” is about 100 for one solution with no bad intermediate prime. The following table gives the expected number (and what we got so far) of “near misses” for one true solution (hit 0) for each “hit” value from 1 to 10.
| k=10 | hit 0 | hit 1 | hit 2 | hit 3 | hit 4 | hit 5 | hit 6 | hit 7 | hit 8 | hit 9 | hit 10 | Total |
| expected | 1 | 5 | 11 | 16 | 19 | 17 | 12 | 8 | 4 | 2 | 1 | 96 |
| got | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | 0 | 0 | 4 |
February 13: Manfred Toplic : N=503744050724614 with 4 bad primes.
March 2 : Manfred Toplic : N=507618446770482 10 PRIMES IN AP !!
March 3 : Robert Piche : N=544044396755080 with 8 bad primes.
9 primes in AP found (not necessarily consecutive)
January 20 : Nik Lygeros and Michel Mizony : N=502501431250729 with 8 bad primes.
January 29 : Nik Lygeros and Michel Mizony : N=500604495345877 with 4 bad primes.
February 2 : J. Ray Ballinger : N=1045277342401 with 9 bad primes.
Nik Lygeros and Michel Mizony : N=522545537725045 with 5 bad primes.
February 4 : Manfred Toplic : N=501791704290455 with 5 bad primes.
February 12 : J. Ray Ballinger : N=41326566104228 with 4 bad primes.
February 20 : Jon Kierkegaard : N=536906684860571 with 9 bad primes.
Jan Roger Sandbakken : N=13562023722693 with 9 bad primes.
February 23 : Tony Forbes : N=309212291995442 with 2 bad primes.
Nik Lygeros and Michel Mizony : N=582041124985537 with 6 bad primes.
February 25 : Jon L. Kierkegaard : N=550606435004925 with 5 bad primes.
February 27 : Manfred Toplic : N=507270760060752 with 7 bad primes.
March 3 : Robert Piche : N=580596232159174 with 2 bad primes. But it is a good one ! 9 consecutive primes in AP. The second solution
8 primes in AP found (not necessarily consecutive)
January 22 : John Lygeros : N=512040795798002 with 5 bad primes.
Tony Forbes : N=303072965929921 with 3 bad primes.
January 28 : Paul Zimmermann : N=224944232660 with 6 bad primes.
January 29 : Alain and Herve Groleau : N=510142046676543 with 5 bad primes.
Jean-Charles Delepine : N=510720315423752 with 4 bad primes.
February 5 : Cyril Aschenbrenner : N=506252124257839 with 3 bad primes.
February 18 : Nicolas Serre : N=524068716581273 with 3 bad primes.
February 20 : Robert Piche : N=544812503241529 with 3 bad primes.
February 23 : Ben Kibel : N=70070509283017 with 2 bad primes, but a New 8 consecutive primes in AP.
February 24 : Juan Toharia Zapata : N=7378592809955 with 2 bad primes.
New 7 consecutive primes in AP
7378592809955, 41547052281388, 309212291995442, 508302781301049, 508850880191424, 510525530867066, 510974359954957, 522722361814050, 530728324530213, 530323512242008, 536880690640184, 538261317599257, 548994191259373, 570754019426504, 572096410510317.