Use the Sieve of Eratosthenes to find all prime numbers betw

Use the Sieve of Eratosthenes to find all prime numbers between 400 and 500. Please list the primes that you are using to implement the Sieve. Find the first seven (even) perfect numbers. You will need the Euclid-Euler Theorem on Even Perfect Numbers, the Sieve of Eratosthenes, the Partial Table of Primes, a calculator, LOTS OF TIME AND LOTS OF PATIENCE. Please use the format presented in class. Use the Euclidean Algorithm to compute the following. gcd(288, 420) gcd(2457, 2200) Derive the formula for the volume of a regular octagon as a function of its side s. It may help to inscribe the regular octagon in a circle.

Solution

Solved the first problem in details, post the problems seperately since they are very big

3) First list all the numbers in the range of 400----500

400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500

Starting with prime number 2 and cutting the numbers which are divisible by 2 we get

401 403 405 407 409 411 413 415 417 419 421 423 425 427 429 431 433 435 437 439 441 443 445 447 449 451 453 455 457 459 461 463 465 467 469 471 473 475 477 479 481 483 485 487 489 491 493 495 497 499

Starting with prime number 3 we get

401 403 407 409 413 415 419 421 425 427 431 433 437 439 443 445 449 451 455 457 461 463 467 469 473 475 479 481 485 487 491 493 497 499

Starting with prine number 5 we get

401 403 407 409 413 419 421 427 431 433 437 439 443 449 451 457 461 463 467 469 473 479 481 487 491 493 497 499

We need to terminate when prime number > sqrt(n) 23

Starting with prime number 7 we get

401 403 407 409 419 421 431 433 437 439 443 449 451 457 461 463 467 473 479 481 487 491 493 499

Starting with prime number 11 we get

401 403 409 419 421 431 433 437 439 443 449 457 461 463 467 479 481 487 491 493 499

Starting with prime number 13 we get

401 409 419 421 431 433 437 439 443 449 457 461 463 467 479 487 491 493 499

With prime number 17

401 409 419 421 431 433 437 439 443 449 457 461 463 467 479 487 491 499

with prime number 19 and prime number 23

401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499