A216145 Primes p such that p (mod 5) = p (mod 7).

2, 3, 37, 71, 73, 107, 109, 179, 211, 281, 283, 317, 353, 389, 421, 457, 491, 563, 599, 631, 701, 739, 773, 809, 877, 911, 947, 983, 1019, 1051, 1087, 1123, 1193, 1229, 1297, 1367, 1439, 1471, 1543, 1579, 1613, 1753, 1787, 1789, 1823, 1997, 1999, 2069, 2137

Offset: 1

Author

Zak Seidov, Sep 02 2012

Keywords

• nonn
• easy

Comments

Or primes p such that p (mod 35) = {1, 2, 3, 4}.

In general if 0 < m (mod p) = m (mod q) then m (mod p*q) < p (with p < q any primes).

Examples

			37 = 2 (mod 5) = 2 (mod 7);
71 = 1 (mod 5) = 1 (mod 7);
73 = 3 (mod 5) = 3 (mod 7);
109 = 4 (mod 5) = 4 (mod 7).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Magma

[p: p in PrimesUpTo(2500) | p mod 5 eq p mod 7]; // Vincenzo Librandi, Jan 17 2016

Maple

select(isprime, [seq(seq(35*i+j,j=1..4),i=0..1000)]); # Robert Israel, Jan 18 2016

Mathematica

Select[Prime[Range[100]],Mod[#,5]==Mod[#,7]&]
Select[Prime[Range[100]],Mod[#,35]<5&]

PARI

isok(n) = isprime(n) && ((n % 5) == (n % 7)); \\ Michel Marcus, Jan 17 2016

PARI

lista(nn) = forprime(p=2, nn, if(p%5 == p%7, print1(p, ", "))); \\ Altug Alkan, Jan 18 2016