353 has primitive roots because it is a prime number. (Not all numbers have primitive roots) It has 160 primitive roots. Generally however when we talk about THE primitive root we are talking about the lowest. So, starting at 2,3,4,5, ...... create a spreadsheet where the columns are the numbers being tested and the rows contain the powers of these numbers modulo 353 up to 176 (=352/2).The first column not containing a 1. is the lowest primitive root.
353% of 1,212 = 4,278.36
Following is a list of all the prime numbers between 300 and 700. All other numbers are multiples. The numbers are copied from the attached link. 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 Between 300 and 700 (not including 300 and 700) there are 399 numbers. Of those, the above 63 are prime. That leaves 336 that are multiples.
353 is not divisible by 9. It is only divisible by 1 and itself because 353 is a prime number.
The numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 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 and 359 are prime.
307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397.
There are sixteen prime numbers between 301 and 400.307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397
They are 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, and 397.
307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397
379
307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367 . . . to infinity.
Two: 353, 359
Prime numbers between 300 and 500 are: 307 311 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499
300
Joe McElderry Decca Records 347- 353, Chiswick road, London, W4 4HS :) put
The prime numbers between 350 and 400 are 353, 359, 367, 373, 379, 383, 389, 397. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In this range, each of these numbers only has two factors: 1 and itself, making them prime.
The factors of 337 are one and itself, as it is prime.