A262098
Primes p such that 2^p + 9 is also prime.
Original entry on oeis.org
2, 3, 5, 7, 23, 37, 47, 263, 317, 3229, 3253
Offset: 1
5 is in sequence because 2^5 + 9 = 41 is prime.
Cf. primes p such that 2^p+k is a prime:
A057736 (k=3),
A175173 (k=5), this sequence (k=9),
A155780 (k=11),
A175234 (k=15),
A262099 (k=17),
A175235 (k=21),
A175236 (k=23),
A262934 (k=27),
A262100 (k=29),
A262201 (k=33),
A262962 (k=35).
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[p: p in PrimesUpTo(1000) | IsPrime(2^p+9)];
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Select[Prime[Range[1000]], PrimeQ[2^# + 9] &]
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for(n=1, 1e3, if(isprime((2^prime(n))+9), print1(prime(n)", "))) \\ Altug Alkan, Sep 18 2015
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use ntheory ":all"; use Math::GMP qw/:constant/; forprimes { say if is_prime(2**$+9) } 10000; # _Dana Jacobsen, Oct 03 2015
A057737
Primes of the form 2^p + 3, where p is prime.
Original entry on oeis.org
7, 11, 131, 147573952589676412931
Offset: 1
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Select[Table[2^p+3, {p, Prime[Range[67]]}], PrimeQ] (* Metin Sariyar, Aug 09 2019 *)
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forprime(p=1, , my(x=2^p+3); if(ispseudoprime(x), print1(x, ", "))) \\ Felix Fröhlich, Aug 09 2019
A153503
Primes p such that 2^(p-1)+3 is prime.
Original entry on oeis.org
2, 3, 5, 7, 13, 17, 19, 29, 31, 229, 2371, 4003, 33029, 55457, 58313, 205963, 1875553
Offset: 1
For p = 2, 2^(p-1)+3 = 5 is prime.
For p = 17, 2^(p-1)+3 = 65539 is prime.
For p = 31, 2^(p-1)+3 = 1073741827 is prime.
Cf.
A057732 (numbers k such that 2^k + 3 is prime),
A057736 (primes p such that 2^p + 3 is prime),
A000043 (primes p such that 2^p - 1 is prime).
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[p: p in PrimesUpTo(2000) | IsPrime(2^(p-1) + 3)]; // Vincenzo Librandi, Jun 09 2015
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Select[Prime[Range[3000]], PrimeQ[2^(# - 1) + 3] &] (* Vincenzo Librandi, Jun 09 2015 *)
A229065
Numbers of the form 2^(p-1)+3, where p is prime.
Original entry on oeis.org
5, 7, 19, 67, 1027, 4099, 65539, 262147, 4194307, 268435459, 1073741827, 68719476739, 1099511627779, 4398046511107, 70368744177667, 4503599627370499, 288230376151711747, 1152921504606846979, 73786976294838206467, 1180591620717411303427, 4722366482869645213699
Offset: 1
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[2^(p-1)+3: p in PrimesUpTo(80)];
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Table[2^(Prime[n] - 1) + 3, {n, 25}]
Showing 1-4 of 4 results.
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