533

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

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 = 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.

∑

n

=

0

10

504

n

{\displaystyle \sum _{n=0}^{10}{504}^{n}}

is prime.

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

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

10

506

−

10

253

−

1

{\displaystyle 10^{506}-10^{253}-1}

510s

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

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

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

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

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

530s

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 = 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 = 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 = 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 = 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).

∑

n

=

0

10

534

n

{\displaystyle \sum _{n=0}^{10}{534}^{n}}

is prime

535 = 5 × 107. It is a Smith number.

34

n

540s

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 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

]

{\displaystyle [5]}

.

4541 - 3541 is prime.

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

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

∑

n

=

0

10

543

n

{\displaystyle \sum _{n=0}^{10}{543}^{n}}

is prime

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. (sequence A331452 in the OEIS)

550s

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

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

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 = 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).

560s

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 = 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

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

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

∑

n

=

0

10

567

n

{\displaystyle \sum _{n=0}^{10}{567}^{n}}

is prime

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.

570s

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

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

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

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

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.

580s

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

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

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 = 2 × 293. It is a 2-Knödel number.

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

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

590s

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

591 = 3 × 197. It is a D-number

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

59264 + 1 is prime

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

597 = 3 × 199. It is a Blum integer

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

4599 - 3599 is prime.