A050539 -id:A050539

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A230527

Numbers n such that 3^6*2^n - 1 is prime.

+10
3

5, 17, 23, 113, 125, 173, 199, 319, 377, 397, 785, 937, 2167, 3785, 3977, 5957, 7727, 8249, 14677, 19577, 20485, 36319, 57509, 60703, 66677, 76877, 77017, 83407, 229405, 1003373

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Riesel Primes with k = 3^6 = 729.

Checked up to n = 1003600.

LINKS

Table of n, a(n) for n=1..30.

K. Bonath, Riesel Prime Database

C. K. Caldwell, 729*2^229405-1

C. K. Caldwell, 729*2^1003373-1

EXAMPLE

729*2^5-1=23327 is a prime number.

MATHEMATICA

b=3^6; i=0; Table[While[i++; cp=b*2^i-1; !PrimeQ[cp]]; i, {j, 1, 15}]

PROG

(PARI) is(n)=ispseudoprime(3^6*2^n-1) \\ Charles R Greathouse IV, May 22 2017

CROSSREFS

Cf. A002235, A002236, A050539, A050566, A050880.

KEYWORD

nonn,hard

AUTHOR

Lei Zhou, Oct 22 2013

EXTENSIONS

Lei Zhou, Nov 08 2013, added a Mathematica program for small elements.

STATUS

approved

A230537

Numbers n such that 3^7*2^n - 1 is prime.

+10
3

1, 2, 6, 13, 22, 29, 30, 33, 36, 50, 61, 118, 180, 226, 405, 433, 522, 789, 929, 960, 1026, 1030, 1118, 1266, 1521, 1718, 2536, 3029, 3366, 4253, 9157, 10165, 23641, 29877, 30648, 47265, 56097, 90501, 101981, 103021, 108370, 117909, 157237, 169156, 174168

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Riesel Primes with k = 3^7 = 2187.

Checked up to n = 1000000.

LINKS

Lei Zhou, Table of n, a(n) for n = 1..52

K. Bonath, Riesel Prime Database

C. K. Caldwell, a(51) = 2187*2^449776-1

C. K. Caldwell, a(52) = 2187*2^916686-1

C. K. Caldwell, a(53) = 2187*2^992632-1

EXAMPLE

2187*2^1-1=4373 is a prime number.

MATHEMATICA

b=3^7; i=0; Table[While[i++; cp=b*2^i-1; !PrimeQ[cp]]; i, {j, 1, 30}]

PROG

(PARI) is(n)=ispseudoprime(3^7*2^n-1) \\ Charles R Greathouse IV, May 22 2017

CROSSREFS

Cf. A002235, A002236, A050539, A050566, A050880, A230527.

KEYWORD

nonn,hard

AUTHOR

Lei Zhou, Oct 22 2013

EXTENSIONS

Lei Zhou, Nov 08 2013, added a Mathematica program for small elements.

STATUS

approved

A032363

Numbers k such that 27*2^k+1 is prime.

+10
2

2, 4, 7, 16, 19, 20, 22, 26, 40, 44, 46, 47, 50, 56, 59, 64, 92, 175, 215, 275, 407, 455, 1076, 1090, 3080, 3322, 6419, 7639, 19360, 30500, 38770, 44164, 50696, 114760, 117784, 153847, 160874, 178739, 379880, 405514, 672007, 974752, 1164664, 1476347, 2218064

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..47

Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300

Ray Ballinger, Proth Search Page

Y. Gallot, Proth.exe: Windows Program for Finding Large Primes

Wilfrid Keller, List of primes k.2^n - 1 for k < 300

Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

PROG

(PARI) is(n)=ispseudoprime(27*2^n+1) \\ Charles R Greathouse IV, Jun 06 2017

CROSSREFS

Cf. A050539 = 27*2^n-1 is prime.

KEYWORD

nonn,hard

AUTHOR

James R. Buddenhagen

EXTENSIONS

More terms from Hugo Pfoertner, Jun 20 2003

More terms from Hugo Pfoertner, Aug 17 2004

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

STATUS

approved

A212311

Numbers n such that 3^8*2^n - 1 is prime.

+10
1

1, 15, 33, 43, 61, 121, 295, 315, 367, 681, 771, 789, 1485, 4915, 5305, 33649, 81343, 85005, 116307, 154869, 230731, 279591, 287847, 329515, 545353, 1053481

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Riesel Primes with k = 3^8 = 6561.

Checked up to n = 1053627.

LINKS

Table of n, a(n) for n=1..26.

K. Bonath,Riesel Prime Database

C. K. Caldwell, 6561*2^1053481-1

EXAMPLE

6561*2^1-1=13121 is a prime number.

MATHEMATICA

b=2^8; i=0; Table[While[i++; cp=b*2^i-1; !PrimeQ[cp]]; i, {j, 1, 13}]

PROG

(PARI) is(n)=ispseudoprime(3^8*2^n-1) \\ Charles R Greathouse IV, Jun 13 2017

CROSSREFS

Cf. A002235, A002236, A050539, A050566, A050880, A230527, A230537.

KEYWORD

nonn,hard

AUTHOR

Lei Zhou, Oct 24 2013

EXTENSIONS

Lei Zhou, Nov 08 2013, added a Mathematica program for small elements.

STATUS

approved

A231374

Numbers n such that 3^9*2^n - 1 is prime.

+10
0

4, 7, 19, 22, 32, 46, 50, 62, 83, 103, 124, 142, 190, 230, 256, 260, 422, 596, 1084, 2270, 2770, 5366, 5434, 5762, 6826, 9239, 15211, 22556, 58790, 81319, 172510, 225350, 236326, 258592, 445364, 975020

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Riesel Primes with k = 3^9 = 19683.

Checked up to n = 1000000.

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

19683*2^4-1=314927 is a prime number.

MATHEMATICA

i=0; Table[While[i++; cp=19683*2^i-1; !PrimeQ[cp]]; i, {j, 1, 20}]

PROG

(PARI) is(n)=ispseudoprime(3^9*2^n-1) \\ Charles R Greathouse IV, Jun 13 2017

CROSSREFS

Cf. A002235, A002236, A050539, A050566, A050880, A230527, A230537, A212311.

KEYWORD

nonn,hard

AUTHOR

Lei Zhou, Nov 08 2013

STATUS

approved

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