
theorem
  5827 is prime
proof
  now
    5827 = 2*2913 + 1; hence not 2 divides 5827 by NAT_4:9;
    5827 = 3*1942 + 1; hence not 3 divides 5827 by NAT_4:9;
    5827 = 5*1165 + 2; hence not 5 divides 5827 by NAT_4:9;
    5827 = 7*832 + 3; hence not 7 divides 5827 by NAT_4:9;
    5827 = 11*529 + 8; hence not 11 divides 5827 by NAT_4:9;
    5827 = 13*448 + 3; hence not 13 divides 5827 by NAT_4:9;
    5827 = 17*342 + 13; hence not 17 divides 5827 by NAT_4:9;
    5827 = 19*306 + 13; hence not 19 divides 5827 by NAT_4:9;
    5827 = 23*253 + 8; hence not 23 divides 5827 by NAT_4:9;
    5827 = 29*200 + 27; hence not 29 divides 5827 by NAT_4:9;
    5827 = 31*187 + 30; hence not 31 divides 5827 by NAT_4:9;
    5827 = 37*157 + 18; hence not 37 divides 5827 by NAT_4:9;
    5827 = 41*142 + 5; hence not 41 divides 5827 by NAT_4:9;
    5827 = 43*135 + 22; hence not 43 divides 5827 by NAT_4:9;
    5827 = 47*123 + 46; hence not 47 divides 5827 by NAT_4:9;
    5827 = 53*109 + 50; hence not 53 divides 5827 by NAT_4:9;
    5827 = 59*98 + 45; hence not 59 divides 5827 by NAT_4:9;
    5827 = 61*95 + 32; hence not 61 divides 5827 by NAT_4:9;
    5827 = 67*86 + 65; hence not 67 divides 5827 by NAT_4:9;
    5827 = 71*82 + 5; hence not 71 divides 5827 by NAT_4:9;
    5827 = 73*79 + 60; hence not 73 divides 5827 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5827 & n is prime
  holds not n divides 5827 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
