7207 = (2 * 3603) + 1 ;
hence not 2 divides 7207 by NAT_4:9; :: thesis:
7207 = (3 * 2402) + 1 ;
hence not 3 divides 7207 by NAT_4:9; :: thesis:
7207 = (5 * 1441) + 2 ;
hence not 5 divides 7207 by NAT_4:9; :: thesis:
7207 = (7 * 1029) + 4 ;
hence not 7 divides 7207 by NAT_4:9; :: thesis:
7207 = (11 * 655) + 2 ;
hence not 11 divides 7207 by NAT_4:9; :: thesis:
7207 = (13 * 554) + 5 ;
hence not 13 divides 7207 by NAT_4:9; :: thesis:
7207 = (17 * 423) + 16 ;
hence not 17 divides 7207 by NAT_4:9; :: thesis:
7207 = (19 * 379) + 6 ;
hence not 19 divides 7207 by NAT_4:9; :: thesis:
7207 = (23 * 313) + 8 ;
hence not 23 divides 7207 by NAT_4:9; :: thesis:
7207 = (29 * 248) + 15 ;
hence not 29 divides 7207 by NAT_4:9; :: thesis:
7207 = (31 * 232) + 15 ;
hence not 31 divides 7207 by NAT_4:9; :: thesis:
7207 = (37 * 194) + 29 ;
hence not 37 divides 7207 by NAT_4:9; :: thesis:
7207 = (41 * 175) + 32 ;
hence not 41 divides 7207 by NAT_4:9; :: thesis:
7207 = (43 * 167) + 26 ;
hence not 43 divides 7207 by NAT_4:9; :: thesis:
7207 = (47 * 153) + 16 ;
hence not 47 divides 7207 by NAT_4:9; :: thesis:
7207 = (53 * 135) + 52 ;
hence not 53 divides 7207 by NAT_4:9; :: thesis:
7207 = (59 * 122) + 9 ;
hence not 59 divides 7207 by NAT_4:9; :: thesis:
7207 = (61 * 118) + 9 ;
hence not 61 divides 7207 by NAT_4:9; :: thesis:
7207 = (67 * 107) + 38 ;
hence not 67 divides 7207 by NAT_4:9; :: thesis:
7207 = (71 * 101) + 36 ;
hence not 71 divides 7207 by NAT_4:9; :: thesis:
7207 = (73 * 98) + 53 ;
hence not 73 divides 7207 by NAT_4:9; :: thesis:
7207 = (79 * 91) + 18 ;
hence not 79 divides 7207 by NAT_4:9; :: thesis:
7207 = (83 * 86) + 69 ;
hence not 83 divides 7207 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 7207 & n is prime holds
not n divides 7207 by XPRIMET1:46;
hence 7207 is prime by NAT_4:14; :: thesis: