300 number: Encyclopedia - 300 number

300 (number)

Three hundred is the natural number following two hundred and ninety-nine and preceding three hundred one.

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300 number - Mathematical properties

It is a triangular number and the sum of a twin prime (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.

300 number - Other fields

Three hundred is

• In bowling, a perfect score, achieved by rolling strikes in all ten frames.
• The title of a comic book by Frank Miller about the Battle of Thermopylae.
• The lowest possible credit score.

For the year, see 300.

300 number - Integers from 301 to 399

301 = 7·43, is the sum of three consecutive primes (97 + 101 + 103).

Moreover, it is a happy number.

It's also HTTP status code indicating the content has been moved and the change is permanent. It's the area code for Maryland.

302 = 2·151, nontotient, also telephone area code for Delaware, also HTTP status code indicating the content has been moved

303 = 3·101, also telephone area code for parts of Colorado, also a proposed HTTP status code

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, also telephone area code for West Virginia, also HTTP code indicated the content has not been modified

305 = 5·61, also telephone area code for parts of Florida

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

307, prime number, Chen prime, also telephone area code for Wyoming

308 = 2^2·7·11, nontotient, Harshad number

309 = 3·103

310 = 2·5·31, sphenic number, noncototient, self number

311 has its own article.

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

313, prime number, palindromic prime, centered square number, also telephone area code for Detroit, Michigan

314 = 2·157, nontotient

315 = 3^2·5·7, Harshad number

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 consecutive primes (103 + 107 + 109), Smith number

320 = 2^6·5, 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

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), Harshad number, untouchable number

325 = 5^2·13, triangular number, hexagonal number, nonagonal number, centered nonagonal number

326 = 2·163, nontotient, noncototient, untouchable number

327 = 3·109; this number appears in all Star Wars movies

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

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

330 = 2·3·5·11, sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67), pentatope number, Harshad number, divisible by the number of primes below it, 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

334 = 2·167, nontotient, self number

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

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

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

343 = 7^3, nice Friedman number since 343 = (3 + 4)^3

344 = 2^3·43, octahedral number, noncototient

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 consecutive primes (79 + 83 + 89 + 97)

349, prime number, sum of consecutive primes (109 + 113 + 127)

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, Eisenstein prime with no imaginary part, Chen prime, palindromic prime, Mertens function returns 0

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

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

360 now has its own article.

361 = 19^2, centered triangular number, centered octagonal number, centered decagonal number, 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

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's 26-gonal and 123-gonal.

367, prime number, self number, strictly non-palindromic number

368 = 2^4·23

369 is the magic constant of the 9×9 magic square; there are 369 free polyominoes of order 8.

370 = 2·5·37, sphenic number, sum of consecutive primes (83 + 89 + 97 + 101), nontotient, Harshad number

371 = 7·53, 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

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

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

375 = 3·5^3, Harshad number, also spur routes of Interstate 75

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

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

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

379, prime number, Chen prime

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

381 = 3·127, sum of the first sixteen primes. Palindrome in base 2 and base 8

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

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

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

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), Harshad number

397, prime number, cuban prime, centered hexagonal number

398 = 2·199, nontotient

399 = 3·7·19, sphenic number, Harshad number

Category: Integers

Adapted from the Wikipedia article "300 number", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki