New Mexico – Before October 7, 2007, The United States state of New Mexico had a single area code of 505. The state was, and still is, referred to as 'the 505' in slang.

506 = 2 × 11 × 23. It is:

507 = 3 × 13², Harshad number in bases 13 and 14.

508 = 2² × 127, sum of four consecutive primes (113 + 127 + 131 + 137), Harshad number in base 13.

509 is:

510 = 2 × 3 × 5 × 17. It is:

511 = 7 × 73. It is:

512 = 2⁹. It is:

513 = 3³ × 19. It is:

514 = 2 × 257, it is:

515 = 5 × 103, it is:

516 = 2² × 3 × 43, it is:

517 = 11 × 47, it is:

518 = 2 × 7 × 37, it is:

519 = 3 × 173, it is:

520 = 2³ × 5 × 13. It is:

521 is:

522 = 2 × 3² × 29. It is:

523 is:

524 = 2² × 131

525 = 3 × 5² × 7. It is:

526 = 2 × 263, centered pentagonal number, nontotient, Smith number

527 = 17 × 31. it is:

528 = 2⁴ × 3 × 11. It is:

529 = 23². It is:

530 = 2 × 5 × 53. It is:

531 = 3² × 59. It is:

532 = 2² × 7 × 19. It is:

533 = 13 × 41. It is:

534 = 2 × 3 × 89. It is:

535 = 5 × 107. It is:

$34n^{3}+51n^{2}+27n+5$ $34n^{3}+51n^{2}+27n+5$ for $n=2$ $n=2$ ; this polynomial plays an essential role in Apéry's proof that $\zeta (3)$ $\zeta (3)$ is irrational.

...
Wikipedia