
theorem
  4889 is prime
proof
  now
    4889 = 2*2444 + 1; hence not 2 divides 4889 by NAT_4:9;
    4889 = 3*1629 + 2; hence not 3 divides 4889 by NAT_4:9;
    4889 = 5*977 + 4; hence not 5 divides 4889 by NAT_4:9;
    4889 = 7*698 + 3; hence not 7 divides 4889 by NAT_4:9;
    4889 = 11*444 + 5; hence not 11 divides 4889 by NAT_4:9;
    4889 = 13*376 + 1; hence not 13 divides 4889 by NAT_4:9;
    4889 = 17*287 + 10; hence not 17 divides 4889 by NAT_4:9;
    4889 = 19*257 + 6; hence not 19 divides 4889 by NAT_4:9;
    4889 = 23*212 + 13; hence not 23 divides 4889 by NAT_4:9;
    4889 = 29*168 + 17; hence not 29 divides 4889 by NAT_4:9;
    4889 = 31*157 + 22; hence not 31 divides 4889 by NAT_4:9;
    4889 = 37*132 + 5; hence not 37 divides 4889 by NAT_4:9;
    4889 = 41*119 + 10; hence not 41 divides 4889 by NAT_4:9;
    4889 = 43*113 + 30; hence not 43 divides 4889 by NAT_4:9;
    4889 = 47*104 + 1; hence not 47 divides 4889 by NAT_4:9;
    4889 = 53*92 + 13; hence not 53 divides 4889 by NAT_4:9;
    4889 = 59*82 + 51; hence not 59 divides 4889 by NAT_4:9;
    4889 = 61*80 + 9; hence not 61 divides 4889 by NAT_4:9;
    4889 = 67*72 + 65; hence not 67 divides 4889 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4889 & n is prime
  holds not n divides 4889 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
