A051663 Primes p such that there is no Carmichael number pqr, p

2, 11, 197, 1223, 1487, 4007, 4547, 7823, 9833, 9839, 10259, 11483, 11807, 11909, 13259, 13967, 14207, 15629, 15803, 16139, 16889, 18287, 19583, 22367, 23039, 23879, 24359, 25349, 29339, 30707, 32027, 33343, 34883, 36929, 38747

Offset: 1

Author

Gilberto Garcia-Pulgarin, Dec 11 1999

Keywords

• nonn

Examples

			2 is a term since there is no Carmichael number of the form 2rq.
		

References

• Gilberto Garcia-Pulgarin, Numeros de Carmichael producto de tes primos, preprint, 1999.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..544 (all terms < 10^6)
• Index entries for sequences related to Carmichael numbers

Programs

PARI

is(p) = {
    for( A=1, p-1,
        my(B=ceil((p^2+1)/A),q,r);
        while(1,
            r=(B*(p+A-1)-p)/(A*B-p*p);
            q=(A*r-A+1)/p;
            if(p>=q, break);
            if(denominator(q)==1 && denominator(r)==1 && r>q && (q*r)%(p-1)==1 && isprime(q) && isprime(r), return(0));
            B++
        )
    );
    1
}; \\ Charles R Greathouse IV, Feb 23 2013

Extensions

Edited by Jack Brennen, Jul 01 2008

Corrected by Emmanuel Vantieghem, Nov 26 2012