let p be Prime; :: thesis: ( not p < 353 or p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 )
assume p < 353 ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 )
then ( 1 + 1 < p + 1 & p < 352 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 349 ) or ( 349 <= p & p <= 349 + 1 ) or ( 350 <= p & p <= 350 + 1 ) or ( 351 <= p & p <= 351 + 1 ) ) by NAT_1:13;

suppose ( 2 <= p & p < 349 ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 )

hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 ) by Ttool349a; :: thesis: verum

end;

suppose ( ( 349 <= p & p <= 349 + 1 ) or ( 350 <= p & p <= 350 + 1 ) or ( 351 <= p & p <= 351 + 1 ) ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 )

then p = 349 by XPRIMES0:350, XPRIMES0:351, XPRIMES0:352, NAT_1:9;
hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 or p = 71 or p = 73 or p = 79 or p = 83 or p = 89 or p = 97 or p = 101 or p = 103 or p = 107 or p = 109 or p = 113 or p = 127 or p = 131 or p = 137 or p = 139 or p = 149 or p = 151 or p = 157 or p = 163 or p = 167 or p = 173 or p = 179 or p = 181 or p = 191 or p = 193 or p = 197 or p = 199 or p = 211 or p = 223 or p = 227 or p = 229 or p = 233 or p = 239 or p = 241 or p = 251 or p = 257 or p = 263 or p = 269 or p = 271 or p = 277 or p = 281 or p = 283 or p = 293 or p = 307 or p = 311 or p = 313 or p = 317 or p = 331 or p = 337 or p = 347 or p = 349 ) ; :: thesis: verum

end;

end;