The sum is:
101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239 + 241 + 251 + 257 + 263 + 269 + 271 + 277 + 281 + 283 + 293 + 307 + 311 + 313 + 317 + 331 + 337 + 347 + 349 + 353 + 359 + 367 + 373 + 379 + 383 + 389 + 397 + 401 + 409 + 419 + 421 + 431 + 433 + 439 + 443 + 449 + 457 + 461 + 463 + 467 + 479 + 487 + 491 + 499 = 20,476
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There are 95 Prime #'s between 1 and 500
The prime numbers between 500 and 600 are : 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593 and 599.
There are (500-100)/2 = 200 numbers divisible by 2 between 100 and 500 counting 100 but not 500. Of these (500-100)/8 = 50 are divisible by 8. So there are 150 numbers between 100 and 500 divisible by two but not by 8. By relative primeness exactly 50 out of these 150 are divisible by 3 and therefore these 50 are exactly the ones divisible by 6 but not by 8.
There are 3 prime numbers between 70 and 80: 71 73 79.
The 17 prime numbers between 400 and 500 are 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, and 499.