reserve a,b,c,k,m,n for Nat;
reserve p for Prime;

theorem
  m satisfies_Sierpinski_problem_76b & m <= 62 implies m in {20,32,51,53,62}
  proof
    assume
A1: m satisfies_Sierpinski_problem_76b;
    assume m <= 62;
    then m = 0 or ... or m = 62;
    then m = 20 or m = 32 or m = 51 or m = 53 or m = 62
    by A1,XPRIMES1:2,13,23,31,41,53,61,71,83,97,101,113,127,131,149,151,163,
    173,181,191,211,223,233,241,251,263,271,281,293,307,311,331,347,353,367,
    373,383,397,401,419,421,431,443,457,461,479,487,491,503,521,541,557,563,
    571,587,593,601,613;
    hence thesis by ENUMSET1:def 3;
  end;
