Five hundred is the natural number following four hundred ninety-nine and preceding five hundred one.

Mathematical Properties

500 is a Harshad number.

Other fields

Five hundred is also

• a card game, see 500 (card game)
• an SMTP status code meaning a syntax error has occurred due to unrecognized command
• the years AD 500, 500 BC.

See also: four hundred, six hundred

501 = 3 × 167, sum of the first eighteen primes, also HTTP status code indicating server does not support facility required, SMTP status code meaning syntax error in parameters

502 = 2 × 251, also a proposed HTTP status code for indicating server is temporarily overloaded, SMTP status code meaning command not implemented

503 prime number, safe prime, sum of three consecutive primes (163 + 167 + 173), sum of the cubes of the first four primes, also a proposed HTTP status code indicating a gateway time-out, SMTP status code meaning bad sequence of commands

504 = 2³ × 3² × 7, tribonacci number, semi-meandric number, Harshad number, also SMTP status code meaning command parameter not implemented

505 = 5 × 101, also telephone area code for New Mexico, also model number of Levi-Straus jeans, model number of Unterseeboot 505

This number is the magic constant of nxn magic square and n-Queens Problem for n = 10.

506 = 2 × 11 × 23, sphenic number, square pyramidal number, pronic number, Harshad number, also telephone area code for New Brunswick

507 = 3 × 13²

508 = 2² × 127, sum of four consecutive primes (113 + 127 + 131 + 137)

509 prime number, Sophie Germain prime, smallest Sophie Germain prime to start a 4-term Cunningham chain of the first kind {509, 1019, 2039, 4079}

510 = 2 × 3 × 5 × 17, sum of eight consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79), sum of ten consecutive primes (31 + 37 + 43 + 47 + 53 + 59 + 61 + 67 + 71), nontotient, Harshad number

511 = 7 × 73, Harshad number

511 is:

• 5-1-1, a transit information hotline in some parts of the United States, including the San Francisco Bay Area.

512 = 2⁹; power of two, Harshad number

513 = 3³ × 19, Harshad number

514 = 2 × 257, centered triangular number, nontotient

515 = 5 × 103, sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)

516 = 2² × 3 × 43, nontotient, untouchable number, Harshad number

517 = 11 × 47, sum of five consecutive primes (97 + 101 + 103 + 107 + 109), Smith number

518 = 2 × 7 × 37 = 5^1 + 1^2 + 8^3 (a property shared with 175 and 598), sphenic number, nontotient, untouchable number, Harshad number

519 = 3 × 173, sum of three consecutive primes (167 + 173 + 179)

520 = 2³ × 5 × 13, untouchable number

521 prime number

522 = 2 × 3² × 29, sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101), Harshad number

523 prime number, sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89)

524 = 2² × 131

525 = 3 × 5² × 7

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

527 = 17 × 31, also the section of the US Tax Code regulating soft money political campaigning (see 527 groups)

528 = 2⁴ × 3 × 11, triangular number

529 = 23², centered octagonal number, also Section 529 of the IRS tax code organizes 529 plans to encourage saving for higher education.

530 = 2 × 5 × 53, sphenic number, nontotient, untouchable number

531 = 3² × 59, Harshad number

532 = 2² × 7 × 19, nontotient

533 = 13 × 41, sum of three consecutive primes (173 + 179 + 181), sum of five consecutive primes (101 + 103 + 107 + 109 + 113)

534 = 2 × 3 × 89, sphenic number, sum of four consecutive primes (127 + 131 + 137 + 139), nontotient

535 = 5 × 107, Smith number

536 = 2³ × 67, the number of ways to arrange the pieces of the stomachion puzzle into a square, not counting rotation or reflection

537 = 3 × 179, Mertens function(537) = 0

538 = 2 × 269, open meandric number, nontotient

539 = 7² × 11

540 = 2² × 3³ × 5, untouchable number, decagonal number, Harshad number

541 prime number, Mertens function(541) = 0, star number

542 = 2 × 271, nontotient

543 = 3 × 181

544 = 2⁵ × 17

545 = 5 × 109, centered square number

546 = 2 × 3 × 7 × 13, sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83)

547 prime number, cuban prime, centered hexagonal number, centered heptagonal number

548 = 2² × 137, nontotient, every positive integer is the sum of at most 548 ninth powers.

549 = 3² × 61

550 = 2 × 5² × 11, pentagonal pyramidal number, nontotient, Harshad number, also SMTP status code meaning the requested action was not taken because the mailbox is unavailable

551 = 19 × 29, sum of three consecutive primes (179 + 181 + 191), SMTP status code meaning user is not local

552 = 2³ × 3 × 23, sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103), sum of ten consecutive primes (37 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73), pronic number, untouchable number, Harshad number; model number of Unterseeboot 552, SMTP status code meaning requested action aborted because the mailbox is full

553 = 7 × 79, sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79); model number of Unterseeboot 553, SMTP status code meaning requested action aborted because of faulty mailbox name

554 = 2 × 277, Mertens function(554) = 6 a record high that stands until 586, nontotient, also SMTP status code meaning transaction failed

555 now has its own page.

556 now has its own page.

557 prime number

558 = 2 × 3² × 31, nontotient, Harshad number, also in the title of the Star Trek: Deep Space Nine episode "The Siege of AR-558"

559 = 13 × 43, sum of five consecutive primes (103 + 107 + 109 + 113 + 127), sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97), nonagonal number, centered cube number, model number of Unterseeboot 559

560 = 2⁴ × 5 × 7, tetrahedral number

561 = 3 × 11 × 17, triangular number, hexagonal number, the first Carmichael number

562 = 2 × 281, Smith number, untouchable number

563 prime number, safe prime, Wilson prime

564 = 2² × 3 × 47, sum of a twin prime (281 + 283)

565 = 5 × 113, sum of three consecutive primes (181 + 191 + 193)

566 = 2 × 283, nontotient

567 = 3⁴ × 7

568 = 2³ × 71, sum of the first nineteen primes

569 prime number

570 = 2 × 3 × 5 × 19

571 prime number, centered triangular number, model number of Unterseeboot 571 which appeared in the 2000 movie U-571

572 = 2² × 11 × 13, nontotient

573 = 3 × 191, model number of Unterseeboot 573

574 = 2 × 7 × 41, sphenic number, nontotient

575 = 5² × 23

576 = 2⁶ × 3² = 24², sum of four consecutive primes (137 + 139 + 149 + 151), highly totient number, Smith number, untouchable number, Harshad number

577 prime number

578 = 2 × 17², nontotient

579 = 3 × 193

580 = 2² × 5 × 29, sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107)

581 = 7 × 83, sum of three consecutive primes (191 + 193 + 197)

582 = 2 × 3 × 97, sphenic number, sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), nontotient

583 = 11 × 53

584 = 2³ × 73, untouchable number

585 = 3² × 5 × 13

586 = 2 × 293, Mertens function(586) = 7 a record high that stands until 1357

587 prime number, safe prime, sum of five consecutive primes (107 + 109 + 113 + 127 + 131)

588 = 2² 3 × 7², Smith number, Harshad number

589 = 19 × 31, sum of three consecutive primes (193 + 197 + 199)

590 = 2 × 5 × 59, sphenic number, nontotient

591 = 3 × 197

592 = 2⁴ × 37, Harshad number

593 prime number, Sophie Germain prime, sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101), sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83)

594 = 2 × 3³ × 11, sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number

595 = 5 × 7 × 17, sphenic number, triangular number, centered nonagonal number

596 = 2² × 149, sum of four consecutive primes (139 + 149 + 151 + 157), nontotient

597 = 3 × 199

598 = 2 × 13 × 23 = 5^1 + 9^2 + 8^3, sphenic number

599 prime number