3947 = (2 * 1973) + 1 ;
hence not 2 divides 3947 by NAT_4:9; :: thesis:
3947 = (3 * 1315) + 2 ;
hence not 3 divides 3947 by NAT_4:9; :: thesis:
3947 = (5 * 789) + 2 ;
hence not 5 divides 3947 by NAT_4:9; :: thesis:
3947 = (7 * 563) + 6 ;
hence not 7 divides 3947 by NAT_4:9; :: thesis:
3947 = (11 * 358) + 9 ;
hence not 11 divides 3947 by NAT_4:9; :: thesis:
3947 = (13 * 303) + 8 ;
hence not 13 divides 3947 by NAT_4:9; :: thesis:
3947 = (17 * 232) + 3 ;
hence not 17 divides 3947 by NAT_4:9; :: thesis:
3947 = (19 * 207) + 14 ;
hence not 19 divides 3947 by NAT_4:9; :: thesis:
3947 = (23 * 171) + 14 ;
hence not 23 divides 3947 by NAT_4:9; :: thesis:
3947 = (29 * 136) + 3 ;
hence not 29 divides 3947 by NAT_4:9; :: thesis:
3947 = (31 * 127) + 10 ;
hence not 31 divides 3947 by NAT_4:9; :: thesis:
3947 = (37 * 106) + 25 ;
hence not 37 divides 3947 by NAT_4:9; :: thesis:
3947 = (41 * 96) + 11 ;
hence not 41 divides 3947 by NAT_4:9; :: thesis:
3947 = (43 * 91) + 34 ;
hence not 43 divides 3947 by NAT_4:9; :: thesis:
3947 = (47 * 83) + 46 ;
hence not 47 divides 3947 by NAT_4:9; :: thesis:
3947 = (53 * 74) + 25 ;
hence not 53 divides 3947 by NAT_4:9; :: thesis:
3947 = (59 * 66) + 53 ;
hence not 59 divides 3947 by NAT_4:9; :: thesis:
3947 = (61 * 64) + 43 ;
hence not 61 divides 3947 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3947 & n is prime holds
not n divides 3947 by XPRIMET1:36;
hence 3947 is prime by NAT_4:14; :: thesis: