# 500 (number)

 ← 499 500 501 →
Cardinal five hundred
Ordinal 500th
(five hundredth)
Factorization 22· 53
Roman numeral D
Binary 1111101002
Ternary 2001123
Quaternary 133104
Quinary 40005
Senary 21526
Octal 7648
Duodecimal 35812
Vigesimal 15020
Base 36 DW36

500 (five hundred) is the natural number following 499 and preceding 501.

## Mathematical properties

500 is a Harshad number.

## Other fields

Five hundred is also

## Slang names

• Monkey (UK slang for £500; USA slang for \$500)[1]

## Numbers from 501 to 599

501 = 3 × 167, the sum of the first 18 primes.

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, Chen prime, Eisenstein prime with no imaginary part, 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, refactorable number, Harshad number, also SMTP status code meaning command parameter not implemented

505 = 5 × 101, also model number of Levi's jeans, model number of U-505

This number is the magic constant of n×n normal magic square and n-queens problem for n = 10.

New Mexico – Before October 7, 2007, The United States state of New Mexico had a single area code[2] of 505. The state was, and still is, referred to as 'the 505' in slang.

506 = 2 × 11 × 23, sphenic number, square pyramidal number, pronic number, Harshad number

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}, Chen prime, Eisenstein prime with no imaginary part, highly cototient number

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 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), nontotient, sparsely totient number, Harshad number.

511 = 7 × 73, Harshad number

511 is:

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, refactorable number, Harshad number

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

518 = 2 × 7 × 37 = 51 + 12 + 83 (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 Lucas prime, Chen prime, Eisenstein prime with no imaginary part

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, also the number of scan lines in the NTSC television standard.

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, sum of totient function for first 41 integers, untouchable number, sum of the first three perfect numbers.

531 = 32 × 59, Harshad number

532 = 22 × 7 × 19, pentagonal number, 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, $34 n^3 + 51 n^2 + 27 n+ 5$ for $n = 2$; this polynomial plays an essential role in Apéry's proof that $\zeta(3)$ is irrational.

535 is used as an abbreviation for May 35, which is used in China instead of June 4 to evade censorship by the Chinese government of references on the Internet to the June Fourth Incident.[3]

536 = 23 × 67, the number of ways to arrange the pieces of the stomachion puzzle into a square, not counting rotation or reflection, refactorable number; lowest happy number beginning with the digit 5.

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

538 = 2 × 269, open meandric number, nontotient; also, the total number of votes in the Electoral College of the United States

539 = 72 × 11

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

541 is the 100th prime, a lucky prime, a Chen prime and the 10th star number. Mertens function(541) = 0.

542 = 2 × 271, nontotient, sum of totient function for first 42 integers

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; also the default port for the Apple Filing Protocol

549 = 32 × 61

550 = 2 × 52 × 11, pentagonal pyramidal number, primitive abundant number, nontotient, Harshad number

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 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73), pronic number, untouchable number, Harshad number; model number of U-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 U-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 is a sphenic number, a repdigit and a Harshad number

556 = 22 × 139, sum of four consecutive primes (131 + 137 + 139 + 149). But it is never the sum of the proper divisors of any integer, making it an untouchable number; happy number; model number of U-556.

557 prime number, Chen prime, Eisenstein prime with no imaginary part

558 = 2 × 32 × 31, nontotient, Harshad number. The sum of the largest prime factors of the first 558 is itself divisible by 558 (the previous such number is 62, the next is 993). Also, 558 is 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 U-559

560 = 24 × 5 × 7, tetrahedral number, refactorable number

561 = 3 × 11 × 17, triangular number, hexagonal number, the first Carmichael number[4]

562 = 2 × 281, Smith number, untouchable number, sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).

• 562 is the number of Native American (including Alaskan) Nations, or "Tribes," recognized by the USA government.

563 103rd prime number, safe prime, Wilson prime, Chen prime, Eisenstein prime with no imaginary part, balanced prime, strictly non-palindromic number, sexy prime, happy number

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

565 = 5 × 113, sum of three consecutive primes (181 + 191 + 193), member of the Mian–Chowla sequence, happy number

566 = 2 × 283, nontotient, happy number

567 = 34 × 7

568 = 23 × 71, sum of the first nineteen primes, refactorable number, smallest number whose seventh power is the sum of 7 seventh powers, the room number booked by Benjamin Braddock in the 1967 film The Graduate, the name of the Student Union bar at Imperial College London

569 prime number, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number

570 = 2 × 3 × 5 × 19

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

572 = 22 × 11 × 13, primitive abundant number, nontotient

573 = 3 × 191, model number of German submarine U-573, known as the Konami number because Konami can be represented by 573's Goroawase form of "ko-na-mi".

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. 576 is also four-dozen sets of a dozen, which makes it 4 gross.

577 prime number, Proth prime

578 = 2 × 172, nontotient

579 = 3 × 193, a ménage number

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, sum of totient function for first 43 integers, refactorable number

585 = 32 × 5 × 13, repdigit in base 8 (1111) (sum of powers of 8 from 0 to 3)

When counting in binary with fingers, expressing 585 as 1001001001, results in the isolation of the index and little fingers of each hand, "throwing up the horns".

586 = 2 × 293, Mertens function(586) = 7 a record high that stands until 1357; also the number of several popular personal computer processors (such as the Intel)

587 prime number, safe prime, sum of five consecutive primes (107 + 109 + 113 + 127 + 131), Chen prime, Eisenstein prime with no imaginary part. Outgoing port for email message submission.

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, pentagonal 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), Eisenstein prime with no imaginary part, balanced prime, Leyland number, member of the Mian–Chowla sequence, strictly non-palindromic number

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 = 51 + 92 + 83, sphenic number

599 prime number, Chen prime, Eisenstein prime with no imaginary part.

## References

1. ^ Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990, ISBN 0-304-34004-9
2. ^ 'Verizon Area Code For New Mexico' http://support.vzw.com/pdf/newmexico_split_map.pdf
3. ^ Larmer, Brook (October 26, 2011). "Where an Internet Joke Is Not Just a Joke". New York Times. Retrieved November 1, 2011.
4. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 14. ISBN 978-1-84800-000-1.