A182475 -id:A182475 - cp's OEIS frontend

A243367 Primes p such that p^2+10 is prime.

3, 7, 11, 13, 31, 53, 59, 71, 83, 97, 101, 127, 151, 157, 179, 181, 211, 223, 227, 239, 311, 367, 379, 449, 487, 521, 599, 601, 613, 619, 631, 743, 773, 809, 827, 883, 977, 1009, 1021, 1039, 1091, 1093, 1103, 1117, 1193, 1201, 1217, 1249, 1427, 1471, 1481, 1483, 1487, 1567

Offset: 1

Zak Seidov, Jun 04 2014

nonn

Cf. A182475.

isok(p) = isprime(p) && isprime(p^2+10); \\ Michel Marcus, Jun 04 2014

a(n) = sqrt(A182475(n)-10).

A182476 Primes of the form p^2+100, where p is prime.

Original entry on oeis.org

109, 149, 269, 389, 461, 941, 1061, 1949, 2309, 2909, 3581, 3821, 10301, 10709, 11549, 11981, 16229, 18869, 19421, 22901, 24749, 26669, 30029, 32141, 44621, 52541, 57221, 72461, 76829, 94349, 96821, 109661, 128981, 134789, 167381, 201701, 214469, 253109

Offset: 1

Alex Ratushnyak, May 01 2012

Cf. A045637 (p^2 + 4 is prime), A079141 (p^2 + 6 is prime), A182475.

Select[Table[p^2 + 100, {p, Prime[Range[200]]}], PrimeQ] (* T. D. Noe, May 01 2012 *)

A217717 Primes of the form x^2 + y^2 - 1, where x and y are primes.

Original entry on oeis.org

7, 17, 73, 97, 193, 241, 313, 337, 409, 457, 577, 1009, 1129, 1201, 1249, 1321, 1489, 1657, 1801, 1873, 2017, 2137, 2377, 2521, 2689, 2833, 2857, 3049, 3169, 3217, 3361, 3529, 3697, 3769, 3889, 4057, 4177, 4441, 4513, 4561, 4657, 5209, 5449, 5569, 5689, 5857

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Mar 21 2013

nonn

Unlike primes of the form x^2+y^2 (A045637) which can be redefined as x^2+4, and primes of the form x^2+y^2+1 (A182475) which can be redefined as primes of the form x^2+10, this sequence appears to have no one-variable analog. In the preceding, x and y are prime.

			457 is in the sequence because it is a prime number, and 457 = 13^2 + 17^2 - 1.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Cf. A045637 (primes of the form p^2+4, where p is prime).

Cf. A182475 (primes of the form p^2+10, where p is prime).

mx = 25; Union[Select[Flatten[Table[Prime[a]^2 + Prime[b]^2 - 1, {a, mx}, {b, a, mx}]], # < Prime[mx]^2 && PrimeQ[#] &]] (* T. D. Noe, Mar 29 2013 *)

A243342 Least prime p that is expressible as the sum of three distinct primes squared in exactly n ways.

Original entry on oeis.org

83, 419, 3779, 10739, 240899, 229979, 1180019, 369419, 36964859, 33670379, 13235699, 21899939, 412547339, 370247939, 467152019, 579994619

Offset: 1

Zak Seidov, Jun 03 2014

All terms are congruent to 5 modulo 6 since the first square must be 9.

			p = 83, {a,b,c} = {3,5,7}, 1 way
p = 419, {a,b,c} = {3,7,19}, {3,11,17}, 2 ways
p = 3779, {a,b,c} ={3,7,61}, {3,17,59}, {3,31,53}, 3 ways
p = 10739, {a,b,c} = {3,11,103}, {3,23,101}, {3,53,89}, {3,67,79}, 4 ways.

Cf. A137364, A182475, A182479.

p = a^2 + b^2 + c^2 with a < b < c primes, note that a = 3 in all cases.

A243368 Primes p such that q = p^2 + 10 and q^2 + 10 are also prime.

Original entry on oeis.org

7, 13, 211, 601, 743, 2281, 2659, 2897, 3109, 3361, 4271, 4397, 6173, 7321, 7351, 8807, 8863, 11941, 12377, 13033, 13159, 13999, 14449, 14951, 20117, 20161, 20551, 22709, 24109, 25733, 27299, 27749, 29989, 30071, 31123, 31541, 33347, 33377, 33487, 33629

Offset: 1

Zak Seidov, Jun 04 2014

nonn

This is a subsequence of A243367 where both p and p^2 + 10 are terms in A243367, see examples.

			p = a(1) = 7 = A243367(2) and p^2 + 10 = 59 = A243367(7),
p = a(2) = 13 = A243367(4) and p^2 + 10 = 179 = A243367(15).

Cf. A182475, A243367.

s=[]; forprime(p=2, 100000, q=p^2+10; if(isprime(q)&&isprime(q^2+10), s=concat(s, p))); s \\ Colin Barker, Jun 04 2014

More terms from Colin Barker, Jun 04 2014

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A243367 Primes p such that p^2+10 is prime.

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A182476 Primes of the form p^2+100, where p is prime.

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A217717 Primes of the form x^2 + y^2 - 1, where x and y are primes.

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A243342 Least prime p that is expressible as the sum of three distinct primes squared in exactly n ways.

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A243368 Primes p such that q = p^2 + 10 and q^2 + 10 are also prime.

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