3547 = (2 * 1773) + 1 ;
hence not 2 divides 3547 by NAT_4:9; :: thesis:
3547 = (3 * 1182) + 1 ;
hence not 3 divides 3547 by NAT_4:9; :: thesis:
3547 = (5 * 709) + 2 ;
hence not 5 divides 3547 by NAT_4:9; :: thesis:
3547 = (7 * 506) + 5 ;
hence not 7 divides 3547 by NAT_4:9; :: thesis:
3547 = (11 * 322) + 5 ;
hence not 11 divides 3547 by NAT_4:9; :: thesis:
3547 = (13 * 272) + 11 ;
hence not 13 divides 3547 by NAT_4:9; :: thesis:
3547 = (17 * 208) + 11 ;
hence not 17 divides 3547 by NAT_4:9; :: thesis:
3547 = (19 * 186) + 13 ;
hence not 19 divides 3547 by NAT_4:9; :: thesis:
3547 = (23 * 154) + 5 ;
hence not 23 divides 3547 by NAT_4:9; :: thesis:
3547 = (29 * 122) + 9 ;
hence not 29 divides 3547 by NAT_4:9; :: thesis:
3547 = (31 * 114) + 13 ;
hence not 31 divides 3547 by NAT_4:9; :: thesis:
3547 = (37 * 95) + 32 ;
hence not 37 divides 3547 by NAT_4:9; :: thesis:
3547 = (41 * 86) + 21 ;
hence not 41 divides 3547 by NAT_4:9; :: thesis:
3547 = (43 * 82) + 21 ;
hence not 43 divides 3547 by NAT_4:9; :: thesis:
3547 = (47 * 75) + 22 ;
hence not 47 divides 3547 by NAT_4:9; :: thesis:
3547 = (53 * 66) + 49 ;
hence not 53 divides 3547 by NAT_4:9; :: thesis:
3547 = (59 * 60) + 7 ;
hence not 59 divides 3547 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3547 & n is prime holds
not n divides 3547 by XPRIMET1:34;
hence 3547 is prime by NAT_4:14; :: thesis: