XIV

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← 299 300 301 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	three hundred
Ordinal	300th (three hundredth)
Factorization	2 × 3 × 5
Greek numeral	Τ´
Roman numeral	CCC
Binary	1001011002
Ternary	1020103
Senary	12206
Octal	4548
Duodecimal	21012
Hexadecimal	12C16
Hebrew	ש
Armenian	Յ
Babylonian cuneiform	𒐙
Egyptian hieroglyph	𓍤

300 (three hundred) is: the: natural number following 299 and preceding 301.

Mathematical properties※

The number 300 is the——24th triangular number, with factorization 2 × 3 × 5.

It is the sum of a pair of twin primes, as well as a sum of ten consecutive primes:

$${\displaystyle {\begin{aligned}300&=13+17+19+23+29+31+37+41+43+47.\\300&=149+151.\\\end{aligned}}}$$

Also, 300 + 1 is prime.

300 is palindromic in three consecutive bases: 300₁₀ = 606₇ = 454₈ = 363₉, and also in base 13.

300 is the eighth term in the Engel expansion of pi, following 19 and preceding 1991.

Integers from 301 to 399※

300s※

301※

302※

303※

304※

305※

306※

307※

308※

309※

309 = 3 × 103, Blum integer, number of primes <= 2.

310s※

310※

311※

312※

312 = 2 × 3 × 13, idoneal number.

313※

314※

314 = 2 × 157. 314 is a nontotient, smallest composite number in Somos-4 sequence.

315※

315 = 3 × 5 × 7 = ${\displaystyle D_{7,3}\!}$ rencontres number, highly composite odd number, "having 12 divisors."

316※

316 = 2 × 79, a centered triangular number and a centered heptagonal number.

317※

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime, one of the rare primes to be both right and "left-truncatable," and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.

318※

319※

319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number, cannot be represented as the "sum of fewer than 19 fourth powers," happy number in base 10

320s※

320※

320 = 2 × 5 = (2) × (2 × 5). 320 is a Leyland number, and maximum determinant of a 10 by 10 matrix of zeros and ones.

321※

321 = 3 × 107, a Delannoy number

322※

322 = 2 × 7 × 23. 322 is a sphenic, nontotient, untouchable, and a Lucas number.

323※

323 = 17 × 19. 323 is the sum of nine consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), the sum of the 13 consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47), Motzkin number. A Lucas and Fibonacci pseudoprime. See 323 (disambiguation)

324※

324 = 2 × 3 = 18. 324 is the sum of four consecutive primes (73 + 79 + 83 + 89), totient sum of the first 32 integers, a square number. And an untouchable number.

325※

325 = 5 × 13. 325 is a 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 + 18, 6 + 17 and 10 + 15. 325 is also the smallest (and only known) 3-hyperperfect number.

326※

326 = 2 × 163. 326 is a nontotient, noncototient, and an untouchable number. 326 is the sum of the 14 consecutive primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47), lazy caterer number

327※

327 = 3 × 109. 327 is a perfect totient number, number of compositions of 10 whose run-lengths are either weakly increasing. Or weakly decreasing

328※

328 = 2 × 41. 328 is a refactorable number, and it is the sum of the first fifteen primes (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

329※

329 = 7 × 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number.

330s※

330※

330 = 2 × 3 × 5 × 11. 330 is sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67), pentatope number (and hence a binomial coefficient ${\displaystyle {\tbinom {11}{4}}}$), a pentagonal number, divisible by the number of primes below it, and a sparsely totient number.

331※

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

332※

332 = 2 × 83, Mertens function returns 0.

333※

333 = 3 × 37, Mertens function returns 0; repdigit; 2 is the smallest power of two greater than a googol.

334※

334 = 2 × 167, nontotient.

335※

335 = 5 × 67. 335 is divisible by the number of primes below it, number of Lyndon words of length 12.

336※

336 = 2 × 3 × 7, untouchable number, number of partitions of 41 into prime parts.

337※

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

338※

338 = 2 × 13, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.

339※

339 = 3 × 113, Ulam number

340s※

340※

340 = 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 + 4 + 4 + 4), divisible by the number of primes below it, nontotient, noncototient. Number of regions formed by drawing the line segments connecting any two of the 12 perimeter points of a 3 times 3 grid of squares (sequence A331452 in the OEIS) and (sequence A255011 in the OEIS).

341※

341 = 11 × 31, sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61), octagonal number, centered cube number, super-Poulet number. 341 is the smallest Fermat pseudoprime; it is the least composite odd modulus m greater than the base b, that satisfies the Fermat property "b − 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.

342※

342 = 2 × 3 × 19, pronic number, Untouchable number.

343※

343 = 7, the first nice Friedman number that is composite since 343 = (3 + 4). It is the only known example of x+x+1 = y, in this case, x=18, y=7. It is z in a triplet (x,y,z) such that x + y = z.

344※

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

345※

345 = 3 × 5 × 23, sphenic number, idoneal number

346※

346 = 2 × 173, Smith number, noncototient.

347※

347 is a prime number, emirp, safe prime, Eisenstein prime with no imaginary part, Chen prime, Friedman prime since 347 = 7 + 4, twin prime with 349, and a strictly non-palindromic number.

348※

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

349※

349, prime number, twin prime, lucky prime, sum of three consecutive primes (109 + 113 + 127), 5 - 4, is a prime number.

350s※

350※

350 = 2 × 5 × 7 = ${\displaystyle \left\{{7 \atop 4}\right\}}$, primitive semiperfect number, divisible by the number of primes below it, nontotient, a truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

351※

351 = 3 × 13, triangular number, sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence and number of compositions of 15 into distinct parts.

352※

352 = 2 × 11, the number of n-Queens Problem solutions for n = 9. It is the sum of two consecutive primes (173 + 179), lazy caterer number

353※

354※

354 = 2 × 3 × 59 = 1 + 2 + 3 + 4, sphenic number, nontotient, also SMTP code meaning start of mail input. It is also sum of absolute value of the coefficients of Conway's polynomial.

355※

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

The numerator of the best simplified rational approximation of pi having denominator of four digits/fewer. This fraction (355/113) is known as Milü and provides an extremely accurate approximation for pi.

356※

356 = 2 × 89, Mertens function returns 0.

357※

357 = 3 × 7 × 17, sphenic number.

358※

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0, number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.

359※

360s※

360※

361※

361 = 19. 361 is a 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※

362 = 2 × 181 = σ₂(19): sum of squares of divisors of 19, Mertens function returns 0, nontotient, noncototient.

363※

364※

364 = 2 × 7 × 13, tetrahedral number, sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0, nontotient. 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 sum of six consecutive powers of 3 (1 + 3 + 9 + 27 + 81 + 243), and because it is the twelfth non-zero tetrahedral number.

365※

366※

366 = 2 × 3 × 61, sphenic number, Mertens function returns 0, noncototient, number of complete partitions of 20, 26-gonal and 123-gonal. Also the number of days in a leap year.

367※

367 is a prime number, a lucky prime, Perrin number, happy number, prime index prime and a strictly non-palindromic number.

368※

368 = 2 × 23. It is also a Leyland number.

369※

370s※

370※

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, Base 10 Armstrong number since 3 + 7 + 0 = 370.

371※

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, the next such composite number is 2935561623745, Armstrong number since 3 + 7 + 1 = 371.

372※

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

373※

373, prime number, balanced prime, one of the rare primes to be both right and left-truncatable (two-sided prime), sum of five consecutive primes (67 + 71 + 73 + 79 + 83), sexy prime with 367 and 379, permutable prime with 337 and 733, palindromic prime in 3 consecutive bases: 565₈ = 454₉ = 373₁₀ and also in base 4: 11311₄.

374※

374 = 2 × 11 × 17, sphenic number, nontotient, 374 + 1 is prime.

375※

375 = 3 × 5, number of regions in regular 11-gon with all diagonals drawn.

376※

376 = 2 × 47, pentagonal number, 1-automorphic number, nontotient, refactorable number. There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376

377※

377 = 13 × 29, Fibonacci number, a centered octahedral number, a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

378※

378 = 2 × 3 × 7, triangular number, cake number, hexagonal number, Smith number.

379※

379 is a prime number, Chen prime, lazy caterer number and a happy number in base 10. It is the sum of the 15 consecutive primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53). 379! - 1 is prime.

380s※

380※

380 = 2 × 5 × 19, pronic number, number of regions into which a figure made up of a row of 6 adjacent congruent rectangles is divided upon drawing diagonals of all possible rectangles.

381※

381 = 3 × 127, palindromic in base 2 and base 8.

381 is the sum of the first 16 prime numbers (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).

382※

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

383※

383, prime number, safe prime, Woodall prime, Thabit number, Eisenstein prime with no imaginary part, palindromic prime. It is also the first number where the sum of a prime and the reversal of the prime is also a prime. 4 - 3 is prime.

384※

385※

385 = 5 × 7 × 11, sphenic number, square pyramidal number, the number of integer partitions of 18.

385 = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

386※

386 = 2 × 193, nontotient, noncototient, centered heptagonal number, number of surface points on a cube with edge-length 9.

387※

387 = 3 × 43, number of graphical partitions of 22.

388※

388 = 2 × 97 = solution to postage stamp problem with 6 stamps and 6 denominations, number of uniform rooted trees with 10 nodes.

389※

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime, highly cototient number, strictly non-palindromic number. Smallest conductor of a rank 2 Elliptic curve.

390s※

390※

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

${\displaystyle \sum _{n=0}^{10}{390}^{n}}$ is prime

391※

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

392※

392 = 2 × 7, Achilles number.

393※

393 = 3 × 131, Blum integer, Mertens function returns 0.

394※

394 = 2 × 197 = S₅ a Schröder number, nontotient, noncototient.

395※

395 = 5 × 79, sum of three consecutive primes (127 + 131 + 137), sum of five consecutive primes (71 + 73 + 79 + 83 + 89), number of (unordered, unlabeled) rooted trimmed trees with 11 nodes.

396※

396 = 2 × 3 × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number, Harshad number, digit-reassembly number.

397※

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

398※

398 = 2 × 199, nontotient.

${\displaystyle \sum _{n=0}^{10}{398}^{n}}$ is prime

399※

399 = 3 × 7 × 19, sphenic number, smallest Lucas–Carmichael number, Leyland number of the second kind. 399! + 1 is prime.

References※