A246519 -id:A246519 - cp's OEIS frontend

A246562 Primes p such that 4+p, 4+p^2, 4+p^3, 4+p^5, and 4+p^7 are all prime.

7, 469363, 2552713, 3378103, 6595597, 6629683, 39837517, 46024063, 46167307, 97371007, 97629403, 105528217, 136983307, 169483033, 202953613, 213792193, 216520987, 216738043, 221705647, 304033927, 317502193, 359133553

Offset: 1

Zak Seidov, Aug 29 2014

nonn

All terms are == {3, 7} mod 10. Subsequence of A246519.

Zak Seidov, Table of n, a(n) for n = 1..60

Cf. A007591, A073573, A125260, A172367, A246519.

Select[Prime[Range[193*10^5]],AllTrue[#^{1,2,3,5,7}+4,PrimeQ]&] (* Harvey P. Dale, Sep 07 2024 *)

forprime(p=1,10^9,if(ispseudoprime(4+p) && ispseudoprime(4+p^2) && ispseudoprime(4+p^3) && ispseudoprime(4+p^5) && ispseudoprime(4+p^7), print1(p,", "))) \\ Derek Orr, Aug 30 2014

A253937 Primes p such that 4+p^7, 4+p^9 and 4+p^11 are also prime.

Original entry on oeis.org

82609, 1032607, 1859479, 2158447, 4952173, 5009593, 5828353, 6779833, 11316859, 11370727, 12786157, 13872853, 14117053, 15082783, 15645697, 15935989, 16715623, 20102569, 21310603, 22106569, 22164253, 23674597, 26012953, 26325613, 29592919, 30086347, 30306637

Offset: 1

K. D. Bajpai, Jan 19 2015

nonn

			a(1) = 82609:
4 + 82609^7 = 26253762656881427836948640304009173;
4 + 82609^9 = 179162157925737357103123335151825463343651893;
4 + 82609^11 = 1222646797417942588836172615268162579679296234658008213;
all four are prime.

K. D. Bajpai, Table of n, a(n) for n = 1..720

Cf. A000040, A125260, A246519, A246562.

Select[Prime[Range[1, 2000000]], PrimeQ[4 + #^7] && PrimeQ[4 + #^9] && PrimeQ[4 + #^11] &]

forprime(p=1, 1e7, if(isprime(4+p^7) && isprime(4+p^9) && isprime(4+p^11), print1(p,", ")))

A243095 Least integer m > 1 such that 4 + m^n is prime or 1 if only 4 + 1^n is prime.

Original entry on oeis.org

3, 3, 3, 1, 7, 3, 7, 1, 3, 3, 9, 1, 33, 7, 9, 1, 43, 17, 27, 1, 9, 3, 7, 1, 55, 47, 285, 1, 27, 3, 39, 1, 43, 117, 163, 1, 63, 255, 15, 1, 87, 3, 43, 1, 187, 77, 37, 1, 105, 45, 25, 1, 99, 305, 79, 1, 3, 27, 903, 1, 127, 293, 255, 1, 27, 27, 435, 1, 207, 143, 127, 1, 117, 295, 1159, 1, 477

Offset: 1

Zak Seidov, Aug 29 2014

nonn

If n is a multiple of 4 then 4 + m^n is prime iff m = 1.

4 + m^(4*x) = (m^(2*x)-2*m^x+2) * (m^(2*x)+2*m^x+2). - Jens Kruse Andersen, Sep 02 2014

Zak Seidov and Jens Kruse Andersen, Table of n, a(n) for n = 1..1000 (first 200 terms from Zak Seidov)

Cf. A007591, A073573, A125260, A172367, A246519.

a(n)=if(n%4==0,return(1));m=2;while(!ispseudoprime(4+m^n),m++);return(m)
vector(100,n,a(n)) \\ Derek Orr, Aug 29 2014

cp's OEIS Frontend

A246562 Primes p such that 4+p, 4+p^2, 4+p^3, 4+p^5, and 4+p^7 are all prime.

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A253937 Primes p such that 4+p^7, 4+p^9 and 4+p^11 are also prime.

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A243095 Least integer m > 1 such that 4 + m^n is prime or 1 if only 4 + 1^n is prime.

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