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 Kosmaj 2006-05-03 15:24

17*2^n-1

k=17 has been reported as continuously tested to n=205,000 but there are 5 more primes found for larger exponents [the largest for n=601158]. With respect to reported n_max, k=17 is by far the largest "hole" in the k<300 group. The intention of this project is to extend the range of tested and reported exponents and to find new primes. k=17, although not a multiple of 3, is a very high-weight k and the probability of new primes for large n's is high. There is also a limited possibility of new primes for n<600k if some ranges were not checked, but there is no way to know.

Since about 3 weeks ago Templus has been sieving k=17 for [I]n[/I] in the 205k - 2M range. The first block, n<300k sieved to 850bn is ready for testing. Please consider testing a file or two if you have an idle machine. Thank you.

[B]Found primes[/B]
17*2^605394-1 (182243 digits) by segmtfault on Sep 19, 2006
17*2^2721830-1 (819354 digits) by unconnected on Oct 17, 2010
17*2^2946584-1 (887012 digits) by pepi37 on May 20, 2013

[B]Status[/B]
[CODE] [URL="http://kosmaj.sakura.ne.jp/rps/17/17_done.txt"]205,000-2,695,000[/URL] RPS - Complete (1 new prime)
2,695,000-2,800,000 unconnected - Complete (17*2^2721830-1 is prime!)
2,800,000-2,840,000 Kosmaj - Complete
2,840,000-2,900,000 unconnected - Complete
2,900,000-2,916,000 RPS - Complete
2,916,000-2,930,000 Kosmaj - Complete
2,930,000-3,000,000 pepi37 - Complete (17*2^2946584-1 is prime!)
3,000,000-3,010,000 Kosmaj - Complete
3,010,000-3,140,000 unconnected - Complete
3,140,000-3,150,000 pepi37 - Complete
3,150,000-3,250,000 unconnected - Complete
3,250,000-3,270,000 Kosmaj - Complete
3,270,000-3,320,000 unconnected - Complete
3,320,000-3,400,000 pepi37 - Complete
3,400,000-3,420,000 SectorX - Complete
3,420,000-3,450,000 Carlos - Complete
3,450,000-3,470,000 SectorX - Complete
3,470,000-3,490,000 Carlos - Complete
3,490,000-3,520,000 SectorX - Complete
3,520,000-3.550,000 kracker - Complete
3,550,000-3,570,000 SectorX - Complete
3,570,000-3,640,000 unconnected - Complete
3,640,000-4,000,000 Thomas11 - Complete
4,000,000-5,000,000 Batalov - Complete (17*2^4107544-1 is prime)
[/CODE][B]Available Files [/B]
Including all candidates in the 3-4M range, including already tested ones.
Extensively sieved by Psieve (latest update of August 19, 2013)
[URL="http://kosmaj.sakura.ne.jp/rps/psieve/k17_3M.zip"]k17_3M.zip[/URL] (39353 candidates)

FFT length of all tests: 192k.

 Kosmaj 2006-05-03 15:29

Known primes

17*2^n-1 primes for following n's are already known. We'll confirm them as we proceed with tests.

[CODE]
211464 confirmed
310744 confirmed
310754 confirmed
429318 confirmed (grobie)
601158 confirmed (Kosmaj)
[/CODE]

 Thomas11 2006-05-03 20:26

I'm taking 250-270 (2 files).

 Kosmaj 2006-05-08 04:08

205-250 complete, 17*2^211464-1 confirmed prime, no other primes found.

Taking 270-280.

 Thomas11 2006-05-08 08:55

250-270 complete, no primes found.

 lsoule 2006-05-10 02:55

Taking 280-290

 lsoule 2006-05-10 21:43

280-290 complete, no primes.
Taking 290-300

 Kosmaj 2006-05-11 15:05

 lsoule 2006-05-11 19:40

290-300 complete, no primes
Taking 300-310

 Kosmaj 2006-05-12 05:15

Taking 310-320.

Edit: 270-280 complete, no primes.

 lsoule 2006-05-12 17:29

300-310 complete, no primes.
Taking 320-330

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