
theorem
  6131 is prime
proof
  now
    6131 = 2*3065 + 1; hence not 2 divides 6131 by NAT_4:9;
    6131 = 3*2043 + 2; hence not 3 divides 6131 by NAT_4:9;
    6131 = 5*1226 + 1; hence not 5 divides 6131 by NAT_4:9;
    6131 = 7*875 + 6; hence not 7 divides 6131 by NAT_4:9;
    6131 = 11*557 + 4; hence not 11 divides 6131 by NAT_4:9;
    6131 = 13*471 + 8; hence not 13 divides 6131 by NAT_4:9;
    6131 = 17*360 + 11; hence not 17 divides 6131 by NAT_4:9;
    6131 = 19*322 + 13; hence not 19 divides 6131 by NAT_4:9;
    6131 = 23*266 + 13; hence not 23 divides 6131 by NAT_4:9;
    6131 = 29*211 + 12; hence not 29 divides 6131 by NAT_4:9;
    6131 = 31*197 + 24; hence not 31 divides 6131 by NAT_4:9;
    6131 = 37*165 + 26; hence not 37 divides 6131 by NAT_4:9;
    6131 = 41*149 + 22; hence not 41 divides 6131 by NAT_4:9;
    6131 = 43*142 + 25; hence not 43 divides 6131 by NAT_4:9;
    6131 = 47*130 + 21; hence not 47 divides 6131 by NAT_4:9;
    6131 = 53*115 + 36; hence not 53 divides 6131 by NAT_4:9;
    6131 = 59*103 + 54; hence not 59 divides 6131 by NAT_4:9;
    6131 = 61*100 + 31; hence not 61 divides 6131 by NAT_4:9;
    6131 = 67*91 + 34; hence not 67 divides 6131 by NAT_4:9;
    6131 = 71*86 + 25; hence not 71 divides 6131 by NAT_4:9;
    6131 = 73*83 + 72; hence not 73 divides 6131 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6131 & n is prime
  holds not n divides 6131 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
