500 (number) explained
500 (five hundred) is the natural number following 499 and preceding 501.
Mathematical properties
500 = 22 × 53. It is an Achilles number and a Harshad number, meaning it is divisible by the sum of its digits. It is the number of planar partitions of 10.
Other fields
Five hundred is also
Slang names
- Monkey (UK slang for £500; US slang for $500)[1]
Integers from 501 to 599
500s
501
See main article: 501 (number). 501 = 3 × 167. It is:
- the sum of the first 18 primes (a term of the sequence).
- palindromic in bases 9 (6169) and 20 (15120).
502
- 502 = 2 × 251
- vertically symmetric number
503
503 is:
- a prime number.
- a safe prime.[2]
- the sum of three consecutive primes (163 + 167 + 173).[3]
- the sum of the cubes of the first four primes.[4]
- a Chen prime[5]
- an Eisenstein prime with no imaginary part.[6]
- an index of a prime Lucas number.
- an isolated prime
504
504 = 23 × 32 × 7. It is:
is prime
[10]
505
506
506 = 2 × 11 × 23. It is:
is a prime number. Its decimal expansion is 252 nines, an eight, and 253 more nines.
507
- 507 = 3 × 132 = 232 - 23 + 1, which makes it a central polygonal number[14]
- The age Ming had before dying.
508
- 508 = 22 × 127, sum of four consecutive primes (113 + 127 + 131 + 137), number of graphical forest partitions of 30,[15] since 508 = 222 + 22 + 2 it is the maximum number of regions into which 23 intersecting circles divide the plane.[16]
509
509 is:
510s
510
510 = 2 × 3 × 5 × 17. 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).
- the sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
- a nontotient.
- a sparsely totient number.[18]
- a Harshad number.
- the number of nonempty proper subsets of an 9-element set.[19]
511
See main article: 511 (number). 511 = 7 × 73. It is:
512
See main article: 512 (number). 512 = 83 = 29. It is:
513
513 = 33 × 19. It is:
- Leyland number of the second kind
- palindromic in bases 2 (10000000012) and 8 (10018)
- a Harshad number
- Area code of Cincinnati, Ohio
514
514 = 2 × 257, it is:
515
515 = 5 × 103, it is:
- the sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
- the number of complete compositions of 11.
516
516 = 22 × 3 × 43, it is:
517
517 = 11 × 47, it is:
- the sum of five consecutive primes (97 + 101 + 103 + 107 + 109).
- a Smith number.[23]
518
518 = 2 × 7 × 37, it is:
- = 51 + 12 + 83 (a property shared with 175 and 598).
- a sphenic number.
- a nontotient.
- an untouchable number.
- palindromic and a repdigit in bases 6 (22226) and 36 (EE36).
- a Harshad number.
519
519 = 3 × 173, it is:
- the sum of three consecutive primes (167 + 173 + 179)
- palindromic in bases 9 (6369) and 12 (37312)
- a D-number.[24]
520s
520
520 = 23 × 5 × 13. It is:
521
521 is:
- a Lucas prime.[25]
- A Mersenne exponent, i.e. 2521−1 is prime.
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- palindromic in bases 11 (43411) and 20 (16120).
4521 - 3521 is prime
522
522 = 2 × 32 × 29. It is:
- the sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101).
- a repdigit in bases 28 (II28) and 57 (9957).
- a Harshad number.
- number of series-parallel networks with 8 unlabeled edges.
523
523 is:
- a prime number.
- the sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89).
- palindromic in bases 13 (31313) and 18 (1B118).
- a prime with a prime number of prime digits
- the smallest prime number that starts a prime gap of length greater than 14
524
524 = 22 × 131
- number of partitions of 44 into powers of 2
525
525 = 3 × 52 × 7. It is palindromic in base ten, as well as the fifty-fifth self number greater than 1 in decimal.[27] It is also:
525 is the number of scan lines in the NTSC television standard.
526
526 = 2 × 263, centered pentagonal number,[30] nontotient, Smith number
527
527 = 17 × 31. It is:
- palindromic in base 15 (25215)
- number of diagonals in a 34-gon[31]
- also, the section of the US Tax Code regulating soft money political campaigning (see 527 groups)
528
528 = 24 × 3 × 11. It is:
529
529 = 232. It is:
530s
530
530 = 2 × 5 × 53. It is:
531
531 = 32 × 59. It is:
- palindromic in base 12 (38312).
- a Harshad number.
- number of 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.[33]
- a nontotient.
- palindromic and a repdigit in bases 11 (44411), 27 (JJ27), and 37 (EE37).
- admirable number.
533
533 = 13 × 41. It is:
- the sum of three consecutive primes (173 + 179 + 181).
- the sum of five consecutive primes (101 + 103 + 107 + 109 + 113).
- palindromic in base 19 (19119).
- generalized octagonal number.
534
534 = 2 × 3 × 89. It is:
- a sphenic number.
- the sum of four consecutive primes (127 + 131 + 137 + 139).
- a nontotient.
- palindromic in bases 5 (41145) and 14 (2A214).
- an admirable number.
is prime
[10] 535
535 = 5 × 107. It is:
for
; this polynomial plays an essential role in
Apéry's proof that
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.[34]
536
536 = 23 × 67. It is:
- the number of ways to arrange the pieces of the ostomachion into a square, not counting rotation or reflection.
- the number of 1's in all partitions of 23 into odd parts
- a refactorable number.
- the lowest happy number beginning with the digit 5.
537
537 = 3 × 179, Mertens function (537) = 0, Blum integer, D-number[24]
538
538 = 2 × 269. It is:
539
539 = 72 × 11
is prime
[10] 540s
540
540 = 22 × 33 × 5. It is:
541
541 is:
.
[40] - 4541 - 3541 is prime.[41]
For the Mertens function,
542
542 = 2 × 271. It is:
543
543 = 3 × 181; palindromic in bases 11 (45411) and 12 (39312), D-number.[24]
is prime
[10] 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.
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:
546
546 = 2 × 3 × 7 × 13. It is:
- the sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
- palindromic in bases 4 (202024), 9 (6669), and 16 (22216).
- a repdigit in bases 9 and 16.
- 546! − 1 is prime.
547
547 is:
548
548 = 22 × 137. It is:
Also, 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)).[47]
550s
550
550 = 2 × 52 × 11. It is:
551
551 = 19 × 29. It is:
- It is the number of mathematical trees on 12 unlabeled nodes.[50]
- the sum of three consecutive primes (179 + 181 + 191).
- palindromic in base 22 (13122).
- the SMTP status code meaning user is not local
552
552 = 23 × 3 × 23. It is:
- the number of prime knots with 11 crossings.
- the sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103).
- the sum of ten consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
- a pronic number.
- an untouchable number.
- palindromic in base 19 (1A119).
- a Harshad number.
- the model number of .
- the SMTP status code meaning requested action aborted because the mailbox is full.
553
553 = 7 × 79. It is:
- the sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
- central polygonal number.[14]
- the model number of .
- the SMTP status code meaning requested action aborted because of faulty mailbox name.
554
554 = 2 × 277. It is:
- a nontotient.
- a 2-Knödel number
- the SMTP status code meaning transaction failed.
Mertens function(554) = 6, a record high that stands until 586.
555
See main article: 555 (number). 555 = 3 × 5 × 37 is:
- a sphenic number.
- palindromic in bases 9 (6769), 10 (55510), and 12 (3A312).
- a repdigit in bases 10 and 36.
- a Harshad number.
- φ(555) = φ(σ(555)).[47]
556
556 = 22 × 139. It is:
- the sum of four consecutive primes (131 + 137 + 139 + 149).
- an untouchable number, because it is never the sum of the proper divisors of any integer.
- a happy number.
- the model number of ; 5.56×45mm NATO cartridge.
557
557 is:
- a prime number.
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- the number of parallelogram polyominoes with 9 cells.
558
558 = 2 × 32 × 31. It is:
- a nontotient.
- a repdigit in bases 30 (II30) and 61 (9961).
- a 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).
- in the title of the episode "The Siege of AR-558"
559
559 = 13 × 43. It is:
- the sum of five consecutive primes (103 + 107 + 109 + 113 + 127).
- the sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97).
- a nonagonal number.[51]
- a centered cube number.[52]
- palindromic in base 18 (1D118).
- the model number of .
560s
560
560 = 24 × 5 × 7. It is:
- a tetrahedral number.[53]
- a refactorable number.
- palindromic in bases 3 (2022023) and 6 (23326).
- the number of diagonals in a 35-gon[31]
561
561 = 3 × 11 × 17. It is:
562
562 = 2 × 281. It is:
- a Smith number.
- an untouchable number.
- the sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
- palindromic in bases 4 (203024), 13 (34313), 14 (2C214), 16 (23216), and 17 (1G117).
- a lazy caterer number .
- the number of Native American (including Alaskan) Nations, or "Tribes," recognized by the USA government.
56264 + 1 is prime
563
563 is:
564
564 = 22 × 3 × 47. It is:
- the sum of a twin prime (281 + 283).
- a refactorable number.
- palindromic in bases 5 (42245) and 9 (6869).
- number of primes <= 212.[59]
565
565 = 5 × 113. It is:
- the sum of three consecutive primes (181 + 191 + 193).
- a member of the Mian–Chowla sequence.[60]
- a happy number.
- palindromic in bases 10 (56510) and 11 (47411).
566
566 = 2 × 283. It is:
567
567 = 34 × 7. It is:
- palindromic in base 12 (3B312).
is prime
[10] 568
568 = 23 × 71. It is:
- the sum of the first nineteen primes (a term of the sequence).
- a refactorable number.
- palindromic in bases 7 (14417) and 21 (16121).
- the 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 number of millilitres in an imperial pint.
- the name of the Student Union bar at Imperial College London
569
569 is:
- a prime number.
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- a strictly non-palindromic number.
570s
570
570 = 2 × 3 × 5 × 19. It is:
- a triangular matchstick number[61]
- a balanced number
571
571 is:
- a prime number.
- a Chen prime.
- a centered triangular number.
- the model number of which appeared in the 2000 movie U-571
572
572 = 22 × 11 × 13. It is:
573
573 = 3 × 191. It is:
- a Blum integer
- known as the Konami number, since "ko-na-mi" is associated with 573 in the Japanese wordplay Goroawase the model number of
574
574 = 2 × 7 × 41. It is:
- a sphenic number.
- a nontotient.
- palindromic in base 9 (7079).
- number of partitions of 27 that do not contain 1 as a part.[62]
- number of amino acid residues in a hemoglobin molecule.
575
575 = 52 × 23. It is:
And the sum of the squares of the first 575 primes is divisible by 575.[64]
576
576 = 26 × 32 = 242. It is:
- the sum of four consecutive primes (137 + 139 + 149 + 151).
- a highly totient number.[65]
- a Smith number.
- an untouchable number.
- palindromic in bases 11 (48411), 14 (2D214), and 23 (12123).
- a Harshad number.
- four-dozen sets of a dozen, which makes it 4 gross.
- a cake number.
- the number of parts in all compositions of 8.[66]
577
577 is:
578
578 = 2 × 172. It is:
- a nontotient.
- palindromic in base 16 (24216).
- area of a square with diagonal 34[68]
579
579 = 3 × 193; it is a ménage number,[69] and a semiprime.
580s
580
580 = 22 × 5 × 29. It is:
- the sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107).
- palindromic in bases 12 (40412) and 17 (20217).
581
581 = 7 × 83. It is:
- the sum of three consecutive primes (191 + 193 + 197).
- a Blum integer
582
582 = 2 × 3 × 97. It is:
- a sphenic number.
- the sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89).
- a nontotient.
- a vertically symmetric number .
- an admirable number.
583
583 = 11 × 53. It is:
- palindromic in base 9 (7179).
- number of compositions of 11 whose run-lengths are either weakly increasing or weakly decreasing[70]
584
584 = 23 × 73. It is:
- an untouchable number.
- the sum of totient function for first 43 integers.
- a refactorable number.
585
585 = 32 × 5 × 13. It is:
- palindromic in bases 2 (10010010012), 8 (11118), and 10 (58510).
- a repdigit in bases 8, 38, 44, and 64.
- 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
See also: 586 (disambiguation). 586 = 2 × 293.
587
587 is:
- a prime number.
- safe prime.
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- the sum of five consecutive primes (107 + 109 + 113 + 127 + 131).
- palindromic in bases 11 (49411) and 15 (29215).
- the outgoing port for email message submission.
- a prime index prime.
588
588 = 22 × 3 × 72. It is:
- a Smith number.
- palindromic in base 13 (36313).
- a Harshad number.
589
589 = 19 × 31. It is:
590s
590
590 = 2 × 5 × 59. It is:
591
591 = 3 × 197, D-number[24]
592
592 = 24 × 37. It is:
- palindromic in bases 9 (7279) and 12 (41412).
- a Harshad number.
59264 + 1 is prime
593
593 is:
- a prime number.
- a Sophie Germain prime.
- the sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101).
- the sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
- an Eisenstein prime with no imaginary part.
- a balanced prime.
- a Leyland prime.
- a member of the Mian–Chowla sequence.
- a strictly non-palindromic number.
594
594 = 2 × 33 × 11. It is:
- the sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
- a nontotient.
- palindromic in bases 5 (43345) and 16 (25216).
- a Harshad number.
- the number of diagonals in a 36-gon.[31]
- a balanced number.
595
595 = 5 × 7 × 17. It is:
596
596 = 22 × 149. It is:
- the sum of four consecutive primes (139 + 149 + 151 + 157).
- a nontotient.
- a lazy caterer number .
597
597 = 3 × 199. It is:
598
598 = 2 × 13 × 23 = 51 + 92 + 83. It is:
- a sphenic number.
- palindromic in bases 4 (211124) and 11 (4A411).
- number of non-alternating permutations of .
599
599 is:
- a prime number.
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- a prime index prime.
4599 - 3599 is prime.
Notes and References
- Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990,
- A005385. Safe primes. 2016-06-11.
- that is, a term of the sequence
- that is, the first term of the sequence
- since 503+2 is a product of two primes, 5 and 101
- since it is a prime which is congruent to 2 modulo 3.
- 2024-05-22 .
- A000073. Tribonacci numbers. 2016-06-11.
- A033950. Refactorable numbers. 2016-06-11.
- 2022-06-02.
- Wohlfahrt. K.. Macbeath's curve and the modular group. Glasgow Math. J.. 27. 1985. 239–247. 0819842 . 10.1017/S0017089500006212. free.
- A000330. Square pyramidal numbers. 2016-06-11.
- A002378. Oblong (or promic, pronic, or heteromecic) numbers. 2016-06-11.
- n^2 - n + 1.
- Sum_ p(k) where p(k) = number of partitions of k (A000041). 2022-05-31.
- n^2 + n + 2.
- A100827. Highly cototient numbers. 2016-06-11.
- A036913. Sparsely totient numbers. 2016-06-11.
- 2^n - 2.
- A061209. Numbers which are the cubes of their digit sum. 2016-06-11.
- A005448. Centered triangular numbers. 2016-06-11.
- A005114. Untouchable numbers. 2016-06-11.
- A006753. Smith numbers. 2016-06-11.
- 1. 2022-05-31.
- A005479. Prime Lucas numbers. 2016-06-11.
- Web site: Many more twin primes below Mersenne exponents than above Mersenne exponents. Dr. Kirkby. Mersenne Forum. May 19, 2021.
- 2024-01-09 .
- 2024-01-09 .
- 2024-01-09 .
- A005891. Centered pentagonal numbers. 2016-06-11.
- n*(n+3)/2. 2022-05-31.
- A016754. Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers. 2016-06-11.
- A000326. Pentagonal numbers. 2016-06-11.
- News: Larmer . Brook . Where an Internet Joke Is Not Just a Joke . November 1, 2011 . New York Times . October 26, 2011.
- A001107. 10-gonal (or decagonal) numbers. 2016-06-11.
- Web site: Prose Edda. Snorri Sturluson. 1880 . 107.
- Web site: Prose Edda. Snorri Sturluson. 1880 . 82.
- A031157. Numbers that are both lucky and prime. 2016-06-11.
- A003154. Centered 12-gonal numbers. Also star numbers. 2016-06-11.
- 2023-10-23 .
- 2023-10-23 .
- Sum_ phi(k), cf. A000010.
- A001844. Centered square numbers. 2016-06-11.
- A002407. Cuban primes. 2016-06-11.
- A003215. Hex (or centered hexagonal) numbers. 2016-06-11.
- A069099. Centered heptagonal numbers. 2016-06-11.
- phi(sigma(k)).
- A002411. Pentagonal pyramidal numbers. 2016-06-11.
- A071395. Primitive abundant numbers. 2016-06-11.
- Web site: Sloane's A000055: Number of trees with n unlabeled nodes. live. 2021-12-19. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. https://web.archive.org/web/20101129012954/http://oeis.org/A000055 . 2010-11-29 .
- A001106. 9-gonal (or enneagonal or nonagonal) numbers. 2016-06-11.
- A005898. Centered cube numbers. 2016-06-11.
- A000292. Tetrahedral numbers. 2016-06-11.
- A000384. Hexagonal numbers. 2016-06-11.
- Book: Higgins, Peter . Number Story: From Counting to Cryptography . limited . 2008 . Copernicus . New York . 978-1-84800-000-1 . 14 .
- A007540. Wilson primes. 2016-06-11.
- A006562. Balanced primes. 2016-06-11.
- A016038. Strictly non-palindromic numbers. 2016-06-11.
- 2^n. 2022-06-02.
- A005282. Mian-Chowla sequence. 2016-06-11.
- 3*n*(n+1)/2.. 2022-06-02.
- 2022-06-02.
- 2022-06-02.
- 2022-06-02.
- A097942. Highly totient numbers. 2016-06-11.
- (n+2)*2^(n-1).
- A080076. Proth primes. 2016-06-11.
- 2*n^2.
- A000179. Ménage numbers. 2016-06-11.
- 2022-06-02.
- A060544. Centered 9-gonal (also known as nonagonal or enneagonal) numbers. 2016-06-11.