A238136 -id:A238136 - cp's OEIS frontend

A243471 Primes p such that p^6 - p^5 + 1 is prime.

3, 31, 73, 181, 367, 373, 523, 631, 733, 1021, 1039, 1171, 1489, 1723, 1777, 2203, 2557, 2683, 3121, 3187, 3319, 4441, 4591, 4621, 4801, 4957, 5113, 5167, 5323, 5431, 5659, 5839, 5851, 5857, 6883, 7057, 7129, 7297, 7309, 7477, 7993, 8017, 8209, 8221, 8689, 8821

Offset: 1

K. D. Bajpai, Jun 05 2014

nonn

			31 appears in the sequence because it is prime and 31^6 - 31^5  + 1 = 858874531 is also prime.
73 appears in the sequence because it is prime and 73^6 - 73^5  + 1 = 149261154697 is also prime.

K. D. Bajpai, Table of n, a(n) for n = 1..5457

Cf. A000040, A091567, A053182, A053183, A053184, A238136.

A243471 := proc() local a, b; a:=ithprime(n); b:= a^6-a^5+1; if isprime (b) then RETURN (a); fi; end: seq(A243471 (), n=1..2000);

c=0; Do[k=Prime[n]; If[PrimeQ[k^6-k^5+1], c++; Print[c," ",k]], {n,1,200000}];

A243472 Primes p such that p^6 - p^5 - 1 is prime.

Original entry on oeis.org

2, 31, 101, 151, 181, 199, 229, 277, 307, 317, 379, 439, 479, 491, 647, 691, 797, 911, 997, 1039, 1051, 1181, 1291, 1367, 1381, 1471, 1511, 1549, 1657, 1709, 1847, 1867, 1987, 2081, 2099, 2111, 2207, 2467, 2621, 2707, 3041, 3221, 3259, 3541, 3571, 3581, 3769

Offset: 1

K. D. Bajpai, Jun 05 2014

nonn

			31 appears in the sequence because it is prime and 31^6 - 31^5 - 1 = 858874529 is also prime.
101 appears in the sequence because it is prime and 101^6 - 101^5  - 1 = 1051010050099 is also prime.

K. D. Bajpai, Table of n, a(n) for n = 1..4699

Cf. A000040, A091567, A053182, A053183, A053184, A238136.

A243472 := proc() local a, b; a:=ithprime(n); b:= a^6-a^5-1; if isprime (b) then RETURN (a); fi; end: seq(A243472 (), n=1..2000);

c = 0;  Do[k=Prime[n]; If[PrimeQ[k^6-k^5-1], c++; Print[c," ",k]], {n,1,200000}];
Select[Prime[Range[600]],PrimeQ[#^6-#^5-1]&] (* Harvey P. Dale, Jan 21 2015 *)

s=[]; forprime(p=2, 4000, if(isprime(p^6-p^5-1), s=concat(s, p))); s \\ Colin Barker, Jun 06 2014

A243522 Primes p such that p^6 - p^5 + 1 and p^6 - p^5 - 1 are both primes.

Original entry on oeis.org

31, 181, 1039, 4591, 13687, 21589, 30211, 40771, 41641, 41947, 55441, 56437, 63559, 70867, 81307, 83407, 83869, 87649, 91639, 111229, 126199, 126499, 134287, 157999, 189559, 201307, 214129, 220699, 225751, 228559, 251431, 281557, 289717, 290839, 323767, 337639

Offset: 1

K. D. Bajpai, Jun 06 2014

nonn

Each term in the sequence yields, by definition, a pair of twin primes. The first term 31 results in 858874531 and 858874529, which are twin primes.

Intersection of A243471 and A243472.

			31 is prime and appears in the sequence because [31^6 -31^5 + 1 =  858874531] and [31^6 -31^5 - 1 =  858874529] are both primes.
181 is prime and appears in the sequence because [181^6 -181^5 + 1 =  34967564082181]  and [181^6 -181^5 - 1 =  34967564082179] are both primes.

K. D. Bajpai, Table of n, a(n) for n = 1..1785

Cf. A000040, A001097, A001359, A006512, A238136.

A243522 := proc() local a,b,d; a:=ithprime(n); b:= a^6-a^5+1; d:= a^6-a^5-1; if isprime (b)and isprime (d) then RETURN (a); fi; end: seq(A243522 (), n=1..30000);

c = 0; a = 2; Do[k = Prime[n]; If[PrimeQ[k^6 - k^5 + 1] && PrimeQ[k^6 - k^5 - 1], c++; Print[c, " ", k]], {n, 1, 2000000}];

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A243471 Primes p such that p^6 - p^5 + 1 is prime.

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A243472 Primes p such that p^6 - p^5 - 1 is prime.

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A243522 Primes p such that p^6 - p^5 + 1 and p^6 - p^5 - 1 are both primes.

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Author

Keywords

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Examples

Links

Crossrefs

Programs

Maple

Mathematica