500 (number)

Template:Other uses Template:More citations needed Template:Use mdy dates Template:Infobox number Template:Wiktionary 500 (five hundred) is the natural number following 499 and preceding 501. Template:TOC limit

Mathematical properties

500 = 2² × 5³. It is an Achilles number, meaning that it is divisible by the squares of its prime factors (i.e. 4 and 25) but is not a power itself, and a Harshad number, meaning it is divisible by the sum of its digits. It is the number of planar partitions of 10.

Integers from 501 to 599

500s

502

502 = 2 × 251. It is a vertically symmetric number.

503

503 is a prime number, a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, an index of a prime Lucas number, and an isolated prime. It is the sum of three consecutive primes (163 + 167 + 173) and the sum of the cubes of the first four primes.

504

504 = 2³ × 3² × 7. It is a tribonacci number, a semi-meandric number, a refactorable number, a Harshad number and a largely composite number. It is the sum of the smallest pair of amicable numbers: (220, 284). The group order of the fourth smallest non-cyclic simple group, A₁(8) = ²G₂(3)′, is 504. There are 504 symmetries of the simple group PSL(2,8) that is the automorphism group of the Macbeath surface.

$\sum _{n=0}^{10}{504}^n$ is prime.

505

505 = 5 × 101. It is the magic constant of n×n normal magic square and n-queens problem for n = 10.

506

506 = 2 × 11 × 23. It is a sphenic number, a square pyramidal number, a pronic number, a Harshad number.

$10^{506}-10^{253}-1$ is a prime number. Its decimal expansion is 252 nines, an eight, and 253 more nines.

507

507 = 3 × 13². it is a central polygonal number because 507=23² - 23 + 1.

508

508 = 2² × 127. It is the sum of four consecutive primes (113 + 127 + 131 + 137). There are 508 graphical forest partitions of 30. Since 508 = 22² + 22 + 2, it is the maximum number of regions into which 23 intersecting circles divide the plane.

509

509 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, a highly cototient number and a prime index prime.

It is a Sophie Germain prime, additionally, it is the smallest Sophie Germain prime to start a 4-term Cunningham chain of the first kind {509, 1019, 2039, 4079}.

510s

510

510 = 2 × 3 × 5 × 17. It is a nontotient, a sparsely totient number, and a Harshad number. There are 510 nonempty proper subsets of an 9-element set.

It is the sum of eight consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79), the sum of ten consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), and the sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).

513

513 = 3³ × 19. It is a Harshad number and a Leyland number of the second kind, using 3 & 6 (3⁶ - 6³). It is palindromic in bases 2 (1000000001₂) and 8 (1001₈).

514

514 = 2 × 257. It is a centered triangular number and a nontotient. It is a palindrome in bases 4 (20002₄), 16 (202₁₆), and 19 (181₁₉).

515

515 = 5 × 103. It is the sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73). There are 515 complete compositions of 11.

516

516 = 2² × 3 × 43. It is a nontotient, an untouchable number, a refactorable number, and a Harshad number.

517

517 = 11 × 47. It is a Smith number and the sum of five consecutive primes (97 + 101 + 103 + 107 + 109).

518

518 = 2 × 7 × 37. It is a sphenic number, a nontotient, an untouchable number, and a Harshad number. It is a repdigit (and is therefore palindromic) in bases 6 (2222₆) and 36 (EE₃₆).

518= 5¹ + 1² + 8³, a property shared with 175 and 598.

519

519 = 3 × 173. It is palindromic in bases 9 (636₉) and 12 (373₁₂), and it is a D-number. It is the sum of three consecutive primes (167 + 173 + 179).

520s

520

520 = 2³ × 5 × 13. It is an untouchable number, an idoneal number, and a palindromic number in base 14 (292₁₄).

521

521 is a prime number, a Lucas prime. a Chen prime, and an Eisenstein prime with no imaginary part. It is palindromic in bases 11 (434₁₁) and 20 (161₂₀).

It is a Mersenne exponent, i.e. 2⁵²¹−1 is prime. It is the largest known such exponent that is the lesser of twin primes.

4⁵²¹ - 3⁵²¹ is prime.

522

522 = 2 × 3² × 29. It is a repdigit in bases 28 (II₂₈) and 57 (99₅₇) and a Harshad number. It is the sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101).

There are 522 series-parallel networks with 8 unlabeled edges.

523

523 is a prime number and a prime with a prime number of prime digits. It is palindromic in bases 13 (313₁₃) and 18 (1B1₁₈). It is the smallest prime number that starts a prime gap of length greater than 14. It is the sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89).

524

524 = 2² × 131. There are 524 partitions of 44 into powers of 2.

525

525 = 3 × 5² × 7. It is a self number, and it is palindromic in base ten.

It is the sum of all prime numbers that divide the orders of the twenty-six sporadic groups (2, 3, 5, ..., 71; aside from 53 and 61).

It is the sum of the dimensions of all five exceptional Lie algebras (14, 52, 78, 133, 248).

526

526 = 2 × 263. It is a centered pentagonal number, a nontotient, and a Smith number.

527

527 = 17 × 31. It is palindromic in base 15 (252₁₅).

There are 527 diagonals in a 34-gon

528

528 = 2⁴ × 3 × 11. It is palindromic in bases 9 (646₉) and 17 (1E1₁₇). It is the 32nd triangular number, and the 167th Totient number.

529

529 = 23². It is a centered octagonal number and a lazy caterer number.

530s

530

530 = 2 × 5 × 53. It is an untouchable number, a sphenic number, and a nontotient. It is palindromic in bases 4 (20102₄), 16 (212₁₆), and 23 (101₂₃). It is the sum of totient function for first 41 integers and the sum of the first three perfect numbers.

531

531 = 3² × 59. It is palindromic in base 12 (383₁₂) and a Harshad number.

There are 531 symmetric matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to 6.

532

532 = 2² × 7 × 19. It is a pentagonal number, a nontotient, and an admirable number. It is a repdigit and thus palindromic in bases 11 (444₁₁), 27 (JJ₂₇), and 37 (EE₃₇).

533

533 = 13 × 41. It is palindromic in base 19 (191₁₉) and a generalized octagonal number. It is the sum of three consecutive primes (173 + 179 + 181) and the sum of five consecutive primes (101 + 103 + 107 + 109 + 113).

534

534 = 2 × 3 × 89. It is a sphenic number, a nontotient and an admirable number. It is palindromic in bases 5 (4114₅) and 14 (2A2₁₄). It is the sum of four consecutive primes (127 + 131 + 137 + 139).

$\sum _{n=0}^{10}{534}^n$ is prime

535

535 = 5 × 107. It is a Smith number.

$34n^3+51n^2+27n+5=535$ 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 Tiananmen Square protests of 1989.

536

536 = 2³ × 67. It is a refactorable number, the 168th Totient number, and the lowest happy number beginning with the digit 5.

There are 536 ways to arrange the pieces of the ostomachion into a square, not counting rotation or reflection.

There are 536 1's in all partitions of 23 into odd parts.

537

537 = 3 × 179. It is a Blum integer, a D-number, and a zero of the Mertens function.

538

538 = 2 × 269. It is a nontotient and an open meandric number.

Other fields:

There are a total of 538 votes in the United States Electoral College. The US political news site, FiveThirtyEight, is a reference to the electoral college.

Radio 538 is a Dutch commercial radio station.

539

539 = 7² × 11.

$\sum _{n=0}^{10}{539}^n$ is prime.

540s

540

540 = 2² × 3³ × 5. It is a largely composite number, an untouchable number, a heptagonal number, and a decagonal number.

It is the sum of a pair of twin primes (269 + 271) and a repdigit in bases 26 (KK₂₆), 29 (II₂₉), 35 (FF₃₅), 44 (CC₄₄), 53 (AA₅₃), and 59 (99₅₉).

541

541 is the 100th prime, a lucky prime, a Chen prime, a zero of the Mertens function and a star number. It is palindromic in bases 18 (1C1₁₈) and 20 (171₂₀). It is the fifth ordered Bell number that represents the number of ordered partitions of $[5]$.

4⁵⁴¹ - 3⁵⁴¹ is prime.

542

542 = 2 × 271. It is a nontotient and the sum of totient function for the first 42 integers.

543

543 = 3 × 181. It is palindromic in bases 11 (454₁₁) and 12 (393₁₂) and a D-number.

$\sum _{n=0}^{10}{543}^n$ is prime

544

544 = 2⁵ × 17. Take a grid of 2 times 5 points. There are 14 points on the perimeter. Join every pair of the perimeter points by a line segment. The lines do not extend outside the grid. 544 is the number of regions formed by these lines. Template:Oeis

544 is also the number of pieces that could be seen in a 5×5×5×5 Rubik's Tesseract. As a standard 5×5×5 has 98 visible pieces (5³ − 3³), a 5×5×5×5 has 544 visible pieces (5⁴ − 3⁴).

545

545 = 5 × 109. It is a centered square number, and it is palindromic in bases 10 (545₁₀) and 17 (1F1₁₇).

546

546 = 2 × 3 × 7 × 13. It is a repdigit in bases 9 and 16, and it is palindromic in bases 4 (20202₄), 9 (666₉), and 16 (222₁₆). It is the sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).

546! − 1 is prime.

547

547 is a prime number, a cuban prime, a centered hexagonal number, a centered heptagonal number, and a prime index prime.

548

548 = 2² × 137. It is a nontotient. Every positive integer is the sum of at most 548 ninth powers.

549

549 = 3² × 61. It is a repdigit in bases 13 (333₁₃) and 60 (99₆₀).

φ(549) = φ(σ(549)).

550s

550

550 = 2 × 5² × 11. It is a pentagonal pyramidal number, a primitive abundant number, a nontotient, and a Harshad number. It is a repdigit in bases 24 (MM₂₄), 49 (BB₄₉), and 54 (AA₅₄).

551

551 = 19 × 29. It is palindromic in base 22 (131₂₂) and the sum of three consecutive primes (179 + 181 + 191).

There are 551 mathematical trees on 12 unlabeled nodes.

552

552 = 2³ × 3 × 23. It is a pronic number, an untouchable number, and a Harshad number. It is palindromic in base 19 (1A1₁₉). It is the sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103) and the sum of ten consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).

There are 552 prime knots with 11 crossings.

553

553 = 7 × 79. It is a central polygonal number and the sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).

554

554 = 2 × 277. It is a nontotient and a 2-Knödel number.

Mertens function(554) = 6, a record high that stands until 586.

555

555= 3 × 5 × 37. It is a sphenic number. It is a repdigit in base 10 and base 36. It is palindromic in bases 9 (676₉), 10 (555₁₀), and 12 (3A3₁₂). Because it is divisible by the sum of its digits (15), it is a Harshad number. It is also a Harshad number in binary, base 11, base 13 and hexadecimal.

555 is also a Moran number, because 555 ÷ (5+5+5) = 555 ÷ 15 = 37, and 37 is prime.

556

556 = 2² × 139. It is a happy number and an untouchable number, because it is never the sum of the proper divisors of any integer. It is the sum of four consecutive primes (131 + 137 + 139 + 149).

557

557 is a prime number, a Chen prime, and an Eisenstein prime with no imaginary part.

There are 557 parallelogram polyominoes with 9 cells.

558

558 = 2 × 3² × 31. It is a nontotient, a Harshad number, and a repdigit in bases 30 (II₃₀) and 61 (99₆₁).

559

559 = 13 × 43. It is a nonagonal number and a centered cube number. It is palindromic in base 18 (1D1₁₈). It is the sum of five consecutive primes (103 + 107 + 109 + 113 + 127) and the sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97).

560s

560

560 = 2⁴ × 5 × 7. It is a tetrahedral number, an octagonal number, and a refactorable number. It is palindromic in bases 3 (202202₃) and 6 (2332₆). There are 560 diagonals in a 35-gon.

562

562 = 2 × 281. It is a Smith number, an untouchable number. and a lazy caterer number. It is palindromic in bases 4 (20302₄), 13 (343₁₃), 14 (2C2₁₄), 16 (232₁₆), and 17 (1G1₁₇). It is the sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).

562⁶⁴ + 1 is prime

563

563 is a prime number a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, a balanced prime, a sexy prime, a happy prime, a prime index prime, and a strictly non-palindromic number. It is the largest known Wilson prime.

5⁵⁶³ - 4⁵⁶³ is prime.

564

564 = 2² × 3 × 47. It is a refactorable number and the sum of a pair of twin primes (281 + 283). It is palindromic in bases 5 (4224₅) and 9 (686₉). There are 564 primes less than or equal to 2¹².

565

565 = 5 × 113. It is a member of the Mian–Chowla sequence and a happy number. It is palindromic in bases 10 (565₁₀) and 11 (474₁₁). It is the sum of three consecutive primes (181 + 191 + 193).

566

566 = 2 × 283. It is a nontotient, a happy number, and a 2-Knödel number.

567

567 = 3⁴ × 7. It is palindromic in base 12 (3B3₁₂).

$\sum _{n=0}^{10}{567}^n$ is prime

568

568 = 2³ × 71. It is a refactorable number, and it is palindromic in bases 7 (1441₇) and 21 (161₂₁). It is the sum of the first nineteen primes. It is the smallest number whose seventh power is the sum of 7 seventh powers.

There are 568 millilitres in an imperial pint.

569

569 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, and a strictly non-palindromic number.

570s

570

570 = 2 × 3 × 5 × 19. It is a triangular matchstick number and a balanced number.

571

571 is a prime number, a Chen prime, and a centered triangular number. There are 571 domino tilings of a 3x10 rectangle.

572

572 = 2² × 11 × 13. It is a primitive abundant number and a nontotient. It is palindromic in bases 3 (210012₃) and 15 (282₁₅).

573

573 = 3 × 191. It is a Blum integer.

It is known as the Konami number, since "ko-na-mi" is associated with 573 in the Japanese wordplay Goroawase.

574

574 = 2 × 7 × 41. It is a sphenic number and a nontotient. It is palindromic in base 9 (707₉). There are 574 partitions of 27 that do not contain 1 as a part.

There are 574 amino acid residues in a hemoglobin molecule.

575

575 = 5² × 23. It is palindromic in bases 10 (575₁₀) and 13 (353₁₃), and it is a centered octahedral number.

The sum of the squares of the first 575 primes is divisible by 575.

576

576 = 2⁶ × 3² = 24². It is a highly totient number, a Smith number, an untouchable number, a Harshad number, and a cake number. It is the sum of four consecutive primes (137 + 139 + 149 + 151). It is palindromic in bases 11 (484₁₁), 14 (2D2₁₄), and 23 (121₂₃). There are 576 parts in all compositions of 8.

577

577 is a prime number, a Proth prime, and a Chen prime. It is palindromic in bases 18 (1E1₁₈) and 24 (101₂₄).

578

578 = 2 × 17². It is palindromic in base 16 (242₁₆), and it is a nontotient. The area of a square with diagonal 34 is 578.

579

579 = 3 × 193. It is a semiprime and a ménage number.

580s

580

580 = 2² × 5 × 29. It is palindromic in bases 12 (404₁₂) and 17 (202₁₇), and it is the sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107).

581

581 = 7 × 83. It is a Blum integer and the sum of three consecutive primes (191 + 193 + 197).

582

582 = 2 × 3 × 97. It is a sphenic number, a nontotient, a vertically symmetric number, and an admirable number. It is the sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89).

583

583 = 11 × 53. It is palindromic in base 9 (717₉). There are 583 compositions of 11 whose run-lengths are either weakly increasing or weakly decreasing.

584

584 = 2³ × 73. It is an untouchable number, a refactorable number and the sum of totient function for first 43 integers.

585

585 = 3² × 5 × 13. It is palindromic in bases 2 (1001001001₂), 8 (1111₈), and 10 (585₁₀). It is a repdigit in bases 8, 38, 44, and 64. It is the 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

586 = 2 × 293. It is a 2-Knödel number.

Mertens function(586) = 7 a record high that stands until 1357.

587

587 is a prime number, a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, and a prime index prime. It is the sum of five consecutive primes (107 + 109 + 113 + 127 + 131). It is palindromic in bases 11 (494₁₁) and 15 (292₁₅).

588

588 = 2² × 3 × 7². It is a Smith number and a Harshad number. It is palindromic in base 13 (363₁₃).

589

589 = 19 × 31. It is a centered tetrahedral number and the sum of three consecutive primes (193 + 197 + 199). It is palindromic in base 21 (171₂₁).

590s

590

590 = 2 × 5 × 59. It is a sphenic number, a pentagonal number, and a nontotient. It is palindromic in base 19 (1C1₁₉).

591

591 = 3 × 197. It is a D-number

592

592 = 2⁴ × 37. It is a Harshad number. It is palindromic in bases 9 (727₉) and 12 (414₁₂).

592⁶⁴ + 1 is prime

593

593 is a prime number. a Sophie Germain prime, an Eisenstein prime with no imaginary part, a balanced prime, a Leyland prime using 2 & 9 (2⁹ + 9²), a member of the Mian–Chowla sequence, and a strictly non-palindromic number. It is the sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101) and the sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).

594

594 = 2 × 3³ × 11. It is a nontotient, a Harshad number, and a balanced number. It is palindromic in bases 5 (4334₅) and 16 (252₁₆). It is the sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79). There are 594 of diagonals in a 36-gon.

595

595 = 5 × 7 × 17. It is a sphenic number, a centered nonagonal number, and the 34th triangular number. It is palindromic in bases 10 (595₁₀) and 18 (1F1₁₈).

596

596 = 2² × 149. It is a nontotient and a lazy caterer number. It is the sum of four consecutive primes (139 + 149 + 151 + 157).

597

597 = 3 × 199. It is a Blum integer

598

598 = 2 × 13 × 23 = 5¹ + 9² + 8³. It is palindromic in bases 4 (21112₄) and 11 (4A4₁₁), and it is a sphenic number. There are 598 non-alternating permutations of {1...6}.

599

599 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, and a prime index prime.

4⁵⁹⁹ - 3⁵⁹⁹ is prime.