Magma code to determine possible candidates for Brands scheme for the Mammon project in a random fasion

random-candidates.magma

bits := 32; batchSize := 100;
p := -1; maxQ := -1;
for i in [1..batchSize] do
    p := RandomPrime(bits);
    phi := EulerPhi(p);
    factors := Factorization(phi);
    q, _ := Max([factor[1] : factor in factors]);
    primitiveCount := EulerPhi(phi);
    if (q gt maxQ) then
       maxQ := q;
       printf "%o, %o, %o\n", p, factors, primitiveCount;
    end if;
end for;