A002255 -id:A002255 - cp's OEIS frontend

A032353 Numbers k such that 7*2^k+1 is prime.

2, 4, 6, 14, 20, 26, 50, 52, 92, 120, 174, 180, 190, 290, 320, 390, 432, 616, 830, 1804, 2256, 6614, 13496, 15494, 16696, 22386, 54486, 88066, 95330, 207084, 283034, 561816, 804534, 811230, 1491852, 2139912, 2167800, 2915954, 3015762, 3511774, 5775996

Offset: 1

James R. Buddenhagen

Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

[n: n in [1..830] | IsPrime(7*2^n+1)]; // Arkadiusz Wesolowski, Feb 24 2017

Select[Range[10^3], PrimeQ[7*2^# + 1] &] (* Michael De Vlieger, Feb 25 2017 *)

is(n)=ispseudoprime(7*2^n+1) \\ Charles R Greathouse IV, Feb 20 2017

Added more terms (from http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html), Joerg Arndt, Apr 07 2013

a(41) from Jeppe Stig Nielsen, Jul 25 2019

A322916 Numbers k such that 303*2^k+1 is prime.

Original entry on oeis.org

1, 2, 5, 8, 9, 10, 13, 17, 21, 30, 38, 93, 125, 140, 170, 178, 181, 394, 453, 588, 1161, 1221, 1573, 1665, 1745, 3613, 3661, 5750, 6002, 6198, 6393, 6764, 7209, 7514, 9444, 13034, 15277, 16070, 20042, 22970, 22977, 25674, 28438, 31040, 35137, 42410, 60285

Offset: 1

Robert Price, Dec 30 2018

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..76 (terms n = 1..68 from Robert Price)
Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

select(n->isprime(303*2^n+1),[$1..1000]); # Muniru A Asiru, Dec 31 2018

Select[Range[1000], PrimeQ[303*2^# + 1] &] (* Robert Price, Dec 30 2018 *)

A322949 Numbers k such that 315*2^k+1 is prime.

Original entry on oeis.org

1, 3, 6, 9, 20, 22, 27, 32, 72, 97, 99, 104, 107, 120, 140, 142, 151, 180, 304, 305, 342, 440, 489, 521, 635, 665, 673, 767, 876, 1040, 1313, 1359, 1764, 2032, 2224, 2280, 2783, 2832, 2875, 5256, 8225, 10297, 11124, 12124, 17552, 18592, 24435, 30704, 37467

Offset: 1

Robert Price, Dec 31 2018

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..77 (terms n = 1..74 from Robert Price)
Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

Select[Range[1000], PrimeQ[315*2^# + 1] &] (* Robert Price, Dec 31 2018 *)

A322957 Numbers k such that 329*2^k+1 is prime.

Original entry on oeis.org

1, 3, 5, 9, 11, 15, 27, 55, 87, 105, 111, 163, 225, 311, 487, 537, 723, 735, 771, 1515, 1599, 4685, 5523, 5895, 9723, 20107, 55035, 66355, 108393, 181189, 455645, 604999, 623005, 829207, 1019093, 1246017, 2099771, 2163717, 2266631, 2348105, 2688221, 3002295

Offset: 1

Robert Price, Dec 31 2018

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..45
Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

select(n->isprime(329*2^n+1),[$1..1000]); # Muniru A Asiru, Dec 31 2018

Select[Range[1000], PrimeQ[329*2^# + 1] &] (* Robert Price, Dec 31 2018 *)

a(37)-a(41) from Jeppe Stig Nielsen, Jan 04 2020

a(42) from Jeppe Stig Nielsen, Dec 20 2024

A322915 Numbers k such that 301*2^k+1 is prime.

Original entry on oeis.org

4, 184, 344, 352, 392, 1060, 2452, 7360, 9736, 10324, 21316, 22752, 27272, 27744, 28068, 55628, 72864, 88472, 95872, 124628, 218584, 424448, 517960, 880792, 1455620, 3284232

Offset: 1

Robert Price, Dec 30 2018

Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

Select[Range[1000], PrimeQ[301*2^# + 1] &] (* Robert Price, Dec 30 2018 *)

a(26) from Jeppe Stig Nielsen, Dec 20 2024

A322922 Numbers k such that 305*2^k+1 is prime.

Original entry on oeis.org

3, 7, 21, 23, 29, 35, 53, 87, 91, 95, 115, 165, 179, 233, 367, 419, 609, 791, 2937, 3713, 4087, 5071, 6497, 30011, 30783, 32861, 48299, 60155, 143623, 293525, 465959, 567161, 975215, 1024223, 1106333, 1285643, 1597089, 2233655, 2733989, 2840155, 3171039

Offset: 1

Robert Price, Dec 30 2018

Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

Select[Range[1000], PrimeQ[305*2^# + 1] &] (* Robert Price, Dec 30 2018 *)

a(38)-a(39) from Jeppe Stig Nielsen, Dec 27 2019
a(40) from Jeppe Stig Nielsen, Feb 05 2020
a(41) from Jeppe Stig Nielsen, Dec 20 2024

A322945 Numbers k such that 307*2^k+1 is prime.

Original entry on oeis.org

2, 8, 16, 26, 34, 112, 182, 226, 304, 782, 6886, 36422, 647786, 1289306, 2862962

Offset: 1

Robert Price, Dec 31 2018

Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

Select[Range[1000], PrimeQ[307*2^# + 1] &] (* Robert Price, Dec 31 2018 *)

a(15) from Jeppe Stig Nielsen, May 30 2020

A322946 Numbers k such that 311*2^k+1 is prime.

Original entry on oeis.org

9, 29, 35, 105, 125, 131, 179, 359, 2735, 28199, 47349, 64485, 1094135, 1171199, 1323071, 2798459, 3037565, 3270759, 3282455

Offset: 1

Robert Price, Dec 31 2018

Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

Select[Range[1000], PrimeQ[311*2^# + 1] &] (* Robert Price, Dec 31 2018 *)

a(16) from Jeppe Stig Nielsen, Dec 27 2019

a(17)-a(20) from Jeppe Stig Nielsen, Dec 20 2024

A322948 Numbers k such that 313*2^k+1 is prime.

Original entry on oeis.org

4, 10, 16, 24, 70, 184, 250, 432, 460, 792, 8482, 9868, 10954, 14098, 16260, 17770, 19354, 81504, 85672, 158662, 166354, 188914, 327924, 337942, 424318, 519748, 621432, 888288, 1949544, 3716716, 3837304, 3869536

Offset: 1

Robert Price, Dec 31 2018

Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255, A050527.

select(n->isprime(313*2^n+1),[$1..1000]); # Muniru A Asiru, Dec 31 2018

Select[Range[1000], PrimeQ[313*2^# + 1] &] (* Robert Price, Dec 31 2018 *)

a(30)-a(32) from Jeppe Stig Nielsen, Dec 20 2024

A322950 Numbers k such that 317*2^k+1 is prime.

Original entry on oeis.org

7, 11, 243, 291, 327, 1211, 7331, 26775, 101603, 171071, 284795, 295195, 323871, 589755, 833467, 1047471

Offset: 1

Robert Price, Dec 31 2018

Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for 300 < k < 600
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002255,A050527.

Select[Range[1000], PrimeQ[317*2^# + 1] &] (* Robert Price, Dec 31 2018 *)

cp's OEIS Frontend

A032353 Numbers k such that 7*2^k+1 is prime.

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A322916 Numbers k such that 303*2^k+1 is prime.

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A322949 Numbers k such that 315*2^k+1 is prime.

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A322957 Numbers k such that 329*2^k+1 is prime.

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A322915 Numbers k such that 301*2^k+1 is prime.

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A322922 Numbers k such that 305*2^k+1 is prime.

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A322945 Numbers k such that 307*2^k+1 is prime.

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A322946 Numbers k such that 311*2^k+1 is prime.

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A322948 Numbers k such that 313*2^k+1 is prime.

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