A181603 Twin primes ending in 1.

11, 31, 41, 61, 71, 101, 151, 181, 191, 241, 271, 281, 311, 421, 431, 461, 521, 571, 601, 641, 661, 811, 821, 881, 1021, 1031, 1051, 1061, 1091, 1151, 1231, 1291, 1301, 1321, 1451, 1481, 1621, 1721, 1871, 1931, 1951, 2081, 2111, 2131, 2141, 2311, 2341, 2381

Offset: 1

Author

Omar E. Pol, Nov 01 2010

Keywords

• base
• nonn

Comments

These are twin primes == 1 (mod 30) or == 11 (mod 30) or == 21 (mod 30). In the first case they cannot be lower twin primes because the upper ones would be == 3 (mod 30) and divisible by 3. In the second case they cannot be upper twin primes because the lower ones would be == 9 (mod 30) and divisible by 3. The last case is excluded because that implies they are divisible by 3. In summary the upper twin primes in here are given by A282326, the lower twin primes in here by A282321. - R. J. Mathar, Feb 14 2017

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos

Crossrefs

Cf. A001097, A181604, A181605, A181606.

Programs

Maple

isA181603 := proc(p)
    if isprime(p) and (isprime(p-2) or isprime(p+2)) then
        if modp(p,10) = 1 then
            true;
        else
            false;
        end if ;
    else
        false;
    end if;
end proc:
for n from 1 to 1000 do
    if isA181603(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Feb 14 2017

Mathematica

Select[Prime@ Range@ 360, Mod[ #, 10] == 1 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)
Select[Flatten[Select[Partition[Prime[Range[400]],2,1],#[[2]]-#[[1]] == 2&]],Mod[#,10]==1&] (* Harvey P. Dale, Oct 24 2021 *)

Extensions

More terms from Robert G. Wilson v, Nov 06 2010