300 (number)

This article is about the number 300, as well as the integers which follow it, up to 399. For other use, see 300 (disambiguation). For the year, see 300. For the British tilting train, see British Rail Class 390. For the Dada magazine, see 391 (magazine). For the automobile, see Volvo 340 and Porsche 356.

300 (three hundred) is the natural number following two hundred ninety-nine and preceding three hundred one.

Mathematical properties

It is a triangular number and the sum of a pair of twin primes (149 + 151), as well as the sum of ten consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). It is a Harshad number.

Other fields

Three hundred is

• The Three Hundred, the name given to the Spartans who fought to the death at the Battle of Thermopylae (although two were sent away prior to the battle and survived, Aristodemus and Pantites)
• Movies about the Three Hundred and the battle:
  • 300 Spartans (1962)
  • 300 (2007)
• In bowling, a perfect score, achieved by rolling strikes in all ten frames (a total of twelve strikes).
• The lowest possible Fair Isaac credit score.
• In cars, Nissan 300ZX

Integers from 301 to 399

301 = 7·43, is the sum of three consecutive primes (97 + 101 + 103), happy number; HTTP status code, indicating the content has been moved and the change is permanent (permanent redirect). It is also the number of a debated Turkish penal code.

302 = 2·151, Nontotient, also a HTTP status code indicating the content has been moved (temporary redirect). Also the displacement of Ford's "5.0" V8.

303 = 3·101, the "See Other" HTTP status code, indicating content can be found elsewhere. Number used for an area code in the Denver Metropolitan area of Colorado.

304 = 2^4·19, sum of six consecutive primes (41 + 43 + 47 + 53 + 59 + 61), sum of eight consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), primitive semiperfect number, untouchable number, nontotient, a HTTP code indicated the content has not been modified, record number of wickets taken in English cricket season by Tich Freeman in 1928.

305 = 5·61, HTTP status code indicating a proxy must be used

306 = 2·3^2·17, sum of four consecutive primes (71 + 73 + 79 + 83), pronic number, Harshad number, untouchable number

307, prime number, Chen prime, HTTP status code for "Temporary Redirect"

308 = 2^2·7·11, Nontotient, totient sum of the first 31 integers, Harshad number.

309 = 3·103

310s

310 = 2.5.31, sphenic number, noncototient, self number

311: see 311 (disambiguation).

312 = 2^3·3·13, Harshad number, self number, Zuckerman number.

313, prime number, palindromic prime, centered square number

314 = 2·157, Nontotient.

315 = 3^2·5·7, Harshad number, Zuckerman number FRE 315 FRE

316 = 2^2·79, centered triangular number, centered heptagonal number

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

318 = 2·3·53, sphenic number, nontotient

319 = 11·29, sum of three consecutive primes (103 + 107 + 109), Smith number, cannot be represented as the sum of fewer than 19 4th powers, Happy number.

320s

320 = 2^6·5 = (2^5)·(2·5), Leyland number, a popular bitrate, maximum determinant of a 10 by 10 matrix of zeros and ones, Harshad number.

321 = 3·107

322 = 2·7·23, sphenic number, nontotient, Harshad number, untouchable number. Also seen as a Skull and Bones reference of power

323 = 17·19, sum of nine consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Motzkin number, self number.

324 = 2^2·3^4 = 18^2, sum of four consecutive primes (73 + 79 + 83 + 89), totient sum of the first 32 integers, untouchable number, Harshad number.

325 = 5^2·13, triangular number, hexagonal number, nonagonal number, centered nonagonal number. 325 is the smallest number to be the sum of two squares in 3 different ways: 1^2 + 18^2 , 6^2 + 17^2 and 10^2 + 15^2.

326 = 2·163, Nontotient, noncototient, untouchable number.

327 = 3·109, perfect totient number; this number appears in all Star Wars movies.

328 = 2^3·41, sum of the first fifteen primes, refactorable number.

329 = 7·47, sum of three consecutive primes (107 + 109 + 113), highly cototient number.

330s

330 = 2·3·5·11, sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67), pentatope number, divisible by the number of primes below it, sparsely totient number, Harshad number, also the number of dimples on a British golf ball.

331, prime number, cuban prime, sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number, centered hexagonal number, Mertens function returns 0.

332 = 2^2·83, Mertens function returns 0.

333 = 3^2·37, Mertens function returns 0, Harshad number. Shorthand for <333, meaning 'MUCH LOVE' (more 3's = more hearts) Symbolically used to represent Choronzon, a demon used in the philosophy of Thelema

334 = 2·167, Nontotient, self number, long-time highest score in test match cricket (held by Sir Donald Bradman and Mark Taylor

335 = 5·67, divisible by the number of primes below it.

336 = 2^4·3·7, Harshad number, untouchable number, also the number of dimples on an American golf ball.

337, prime number, permutable prime with 373 and 733, Chen prime, star number

338 = 2·13^2, Nontotient.

339 = 3·113

340s

340 = 2^2·5·17, sum of eight consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), sum of ten consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), sum of the first four powers of 4 (4^1 + 4^2 + 4^3 + 4^4), divisible by the number of primes below it, nontotient, noncototient.

341 = 11·31, sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61), octagonal number, centered cube number, super-Poulet number. 341 = 11·31 is the least composite odd modulus m greater than the base b, that satisfies the Fermat property "b^(m-1) - 1 is divisible by m", for bases less than 100 of b = 2, 15, 60, 63 and 78.

342 = 2·3^2·19, pronic number, Harshad number, untouchable number.

343 = 7^3, nice Friedman number since 343 = (3 + 4)^3. It is z in a triplet (x,y,z) such that x^5 + y^2 = z^3. The number of New York City Firefighters who died September 11, 2001. The number of the monitor of Installation 04 (343 Guilty Spark) in the Halo series of games.

344 = 2^3·43, octahedral number, noncototient, totient sum of the first 33 integers, refactorable number.

345 = 3·5·23, sphenic number, self number.

346 = 2·173, Smith number, noncototient.

347, prime number, safe prime, Eisenstein prime with no imaginary part, Chen prime, Friedman number since 347 = 7^3 + 4, strictly non-palindromic number.

348 = 2^2·3·29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.

349, prime number, sum of three consecutive primes (109 + 113 + 127), the number of seats in the Swedish parliament.

350s

350 = 2·5^2·7, primitive semiperfect number, divisible by the number of primes below it, nontotient.

351 = 3^3·13, triangular number, sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence, Harshad number.

352 = 2^5·11, the number of n-Queens Problem solutions for n = 9.

353, prime number, Chen prime, Proth prime, Eisenstein prime with no imaginary part, palindromic prime, Mertens function returns 0. 353 is the smallest 4th power that is the sum of 4 other 4th powers, discovered by Norrie in 1911: 353^4 = 30^4 + 120^4 + 272^4 + 215^4.

354 = 2·3·59, sphenic number, nontotient, also SMTP code meaning start of mail input.

355 = 5·71, Smith number, Mertens function returns 0, divisible by the number of primes below it.

356 = 2^2·89, Mertens function returns 0, self number.

357 = 3·7·17, sphenic number.

358 = 2·179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0. (358) Also Known as Viktor Lara in Southern Texas.

359, prime number, safe prime, Eisenstein prime with no imaginary part, Chen prime, strictly non-palindromic number.

360s

360, has its own article.

361 = 19^2, centered triangular number, centered octagonal number, centered decagonal number, member of the Mian-Chowla sequence; also the number of positions on a standard 19 x 19 Go board.

362 = 2·181, Mertens function returns 0, nontotient, noncototient.

363 = 3·11^2, sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Mertens function returns 0, perfect totient number.

364 = 2^2·7·13, tetrahedral number, Mertens function returns 0, nontotient, Harshad number. It is a repdigit in base 3 (111111), base 9 (444), base 25 (EE), base 27 (DD), base 51 (77) and base 90 (44). The total number of gifts received in the song "The Twelve Days of Christmas".

365 = 5·73 = 10^2 + 11^2 + 12^2 = 13^2 + 14^2, centered square number, the approximate number of solar days in a tropical year. Several varieties of calendar have resulted from attempts to divide the 29.5-day lunar month and traditional 7-day week into the 365.25 day year.

366 = 2·3·61, sphenic number, Mertens function returns 0, noncototient. Also, the number of days in a leap year; it is 26-gonal and 123-gonal.

367, Is a prime number, self number and a strictly non-palindromic number.

368 = Is 2^4·23, it is also a Leyland number.

369 is the magic constant of the 9×9 normal magic square and n-Queens Problem for n = 9; there are 369 free polyominoes of order 8. With 370, a Ruth-Aaron pair with only distinct prime factors counted.

370s

370 = Armstrong number since 3³ + 7³ + 0³ = 370, 2·5·37, sphenic number, sum of four consecutive primes (83 + 89 + 97 + 101), Nontotient, with 369 part of a Ruth-Aaron pair with only distinct prime factors counted, Harshad number.

371 = 7·53, Armstrong number since 3³ + 7³ + 1³ = 371, sum of three consecutive primes (113 + 127 + 131), sum of seven consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67), sum of the primes from its least to its greatest prime factor (sequence A055233 in OEIS), the next such composite number is 2935561623745.

372 = 2^2·3·31, sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Harshad number, noncototient, untouchable number, refactorable number.

373, prime number, balanced prime, sum of five consecutive primes (67 + 71 + 73 + 79 + 83), permutable prime with 337 and 733, palindromic prime.

374 = 2·11·17, sphenic number, nontotient.

375 = 3·5^3, Harshad number

376 = 2^3·47, 1-automorphic number, nontotient, refactorable number.

377 = 13·29, Fibonacci number, sum of the squares of the first six primes.

378 = 2·3^3·7, triangular number, hexagonal number, Smith number, Harshad number, self number.

379, prime number, Chen prime.

380s

380 = 2^2·5·19, pronic number, also, model number of the Airbus A380, the largest aircraft as of 2005.

381 = 3·127, sum of the first sixteen primes. Palindrome in base 2 and base 8. Represents the term "I Love You", (3) words, (8) letters, (1) meaning.

382 = 2·191, sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Smith number.

383, prime number, safe prime, Woodall prime, Thabit number, Eisenstein prime with no imaginary part, palindromic prime.

384 = 2^7·3, sum of a twin prime (191 + 193), sum of six consecutive primes (53 + 59 + 61 + 67 + 71 + 73), double factorial of 8, sum of the totient sums of the first 35 integers, refactorable number, Zuckerman number.

385 = 5·7·11, sphenic number, square pyramidal number.

386 = 2·193, Nontotient, noncototient, nonagonal number, centered heptagonal number, also shorthand for the Intel 80386 microprocessor chip. 386 generation refers to South Koreans, especially politicians, born in the '60s (ko:386 세대). Number of Pokémon in 3rd Generation National Pokédex.

387 = 3^2·43, also shorthand for the Intel 80387, math coprocessor chip to the 386.

388 = 2^2·97

389, prime number, Eisenstein prime with no imaginary part, Chen prime, highly cototient number, self number, strictly non-palindromic number. Also, 389 equals the displacement in cubic inches of the famous Pontiac GTO V-8 engine of 1964-1966. Smallest conductor of a rank 2 Elliptic curve.

390s

390 = 2·3·5·13, sum of four consecutive primes (89 + 97 + 101 + 103), nontotient.

391 = 17·23, Smith number, centered pentagonal number.

392 = 2^3·7^2, Harshad number.

393 = 3·131, Mertens function returns 0.

394 = 2·197, Nontotient, noncototient.

395 = 5·79, sum of three consecutive primes (127 + 131 + 137), sum of five consecutive primes (71 + 73 + 79 + 83 + 89).

396 = 2^2·3^2·11, sum of a twin prime (197 + 199), totient sum of the first 36 integers, refactorable number, Harshad number.

397, prime number, cuban prime, centered hexagonal number.

398 = 2·199, Nontotient.

399 = 3·7·19, sphenic number, smallest Lucas-Carmichael number, Harshad number.

ca:Tres-cents

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