300 (number)

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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	22 × 3 × 52
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.

300 is a composite number.

315 = 3² × 5 × 7 = ${\displaystyle D_{7,3}\!}$, rencontres number, highly composite odd number, having 12 divisors.^[1]

316 = 2² × 79, a centered triangular number^[2] and a centered heptagonal number.^[3]

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,^[4] one of the rare primes to be both right and left-truncatable,^[5] and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.^[6]

319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number,^[7] cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10^[8]

320 = 2⁶ × 5 = (2⁵) × (2 × 5). 320 is a Leyland number,^[9] and maximum determinant of a 10 by 10 matrix of zeros and ones.

321 = 3 × 107, a Delannoy number^[10]

322 = 2 × 7 × 23. 322 is a sphenic,^[11] nontotient, untouchable,^[12] and a Lucas number.^[13] It is also the first unprimeable number to end in 2.

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.^[14] A Lucas and Fibonacci pseudoprime. See 323 (disambiguation)

324 = 2² × 3⁴ = 18². 324 is the sum of four consecutive primes (73 + 79 + 83 + 89), totient sum of the first 32 integers, a square number,^[15] and an untouchable number.^[12]

325 = 5² × 13. 325 is a triangular number, hexagonal number,^[16] nonagonal number,^[17] and a centered nonagonal number.^[18] 325 is the smallest number to be the sum of two squares in 3 different ways: 1² + 18², 6² + 17² and 10² + 15². 325 is also the smallest (and only known) 3-hyperperfect number.^[19][20]

326 = 2 × 163. 326 is a nontotient, noncototient,^[21] and an untouchable number.^[12] 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^[22]

327 = 3 × 109. 327 is a perfect totient number,^[23] number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing^[24]

328 = 2³ × 41. 328 is a refactorable number,^[25] 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 = 7 × 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number.^[26]

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,^[27] divisible by the number of primes below it, and a sparsely totient number.^[28]

331 is a prime number, super-prime, cuban prime,^[29] a lucky prime,^[30] sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,^[31] centered hexagonal number,^[32] and Mertens function returns 0.^[33]

332 = 2² × 83, Mertens function returns 0.^[33]

333 = 3² × 37, Mertens function returns 0;^[33] repdigit; 2³³³ is the smallest power of two greater than a googol.

334 = 2 × 167, nontotient.^[34]

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

336 = 2⁴ × 3 × 7, untouchable number,^[12] number of partitions of 41 into prime parts,^[35] largely composite number.^[36]

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,^[4] star number

338 = 2 × 13², nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.^[37]

339 = 3 × 113, Ulam number^[38]

340 = 2² × 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 (4¹ + 4² + 4³ + 4⁴), divisible by the number of primes below it, nontotient, noncototient.^[21] 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 = 11 × 31, sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61), octagonal number,^[39] centered cube number,^[40] 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^m−1 − 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.

342 = 2 × 3² × 19, pronic number,^[41] Untouchable number.^[12]

343 = 7³, the first nice Friedman number that is composite since 343 = (3 + 4)³. It is the only known example of x²+x+1 = y³, in this case, x=18, y=7. It is z³ in a triplet (x,y,z) such that x⁵ + y² = z³.

344 = 2³ × 43, octahedral number,^[42] noncototient,^[21] totient sum of the first 33 integers, refactorable number.^[25]

345 = 3 × 5 × 23, sphenic number,^[11] idoneal number

346 = 2 × 173, Smith number,^[7] noncototient.^[21]

347 is a prime number, emirp, safe prime,^[43] Eisenstein prime with no imaginary part, Chen prime,^[4] Friedman prime since 347 = 7³ + 4, twin prime with 349, and a strictly non-palindromic number.

348 = 2² × 3 × 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.^[25]

349, prime number, twin prime, lucky prime, sum of three consecutive primes (109 + 113 + 127), 5³⁴⁹ - 4³⁴⁹ is a prime number.^[44]

350 = 2 × 5² × 7 = ${\displaystyle \left\{{7 \atop 4}\right\}}$, primitive semiperfect number,^[45] divisible by the number of primes below it, nontotient, a truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

351 = 3³ × 13, triangular number, sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence^[46] and number of compositions of 15 into distinct parts.^[47]

352 = 2⁵ × 11, the number of n-Queens Problem solutions for n = 9. It is the sum of two consecutive primes (173 + 179), lazy caterer number^[22]

354 = 2 × 3 × 59 = 1⁴ + 2⁴ + 3⁴ + 4⁴,^[48][49] sphenic number,^[11] nontotient, also SMTP code meaning start of mail input. It is also sum of absolute value of the coefficients of Conway's polynomial.

355 = 5 × 71, Smith number,^[7] Mertens function returns 0,^[33] divisible by the number of primes below it.^[50] The cototient of 355 is 75,^[51] where 75 is the product of its digits (3 x 5 x 5 = 75).

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

356 = 2² × 89, Mertens function returns 0.^[33]

357 = 3 × 7 × 17, sphenic number.^[11]

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,^[33] number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.^[52]

361 = 19². 361 is a centered triangular number,^[2] centered octagonal number, centered decagonal number,^[53] member of the Mian–Chowla sequence;^[54] also the number of positions on a standard 19 x 19 Go board.

362 = 2 × 181 = σ₂(19): sum of squares of divisors of 19,^[55] Mertens function returns 0,^[33] nontotient, noncototient.^[21]

364 = 2² × 7 × 13, tetrahedral number,^[56] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,^[33] 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.^[56]

366 = 2 × 3 × 61, sphenic number,^[11] Mertens function returns 0,^[33] noncototient,^[21] number of complete partitions of 20,^[57] 26-gonal and 123-gonal. Also the number of days in a leap year.

367 is a prime number, a lucky prime,^[30] Perrin number,^[58] happy number, prime index prime and a strictly non-palindromic number.

368 = 2⁴ × 23. It is also a Leyland number.^[9]

370 = 2 × 5 × 37, sphenic number,^[11] 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 3³ + 7³ + 0³ = 370.

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,^[59] the next such composite number is 2935561623745, Armstrong number since 3³ + 7³ + 1³ = 371.

372 = 2² × 3 × 31, sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), noncototient,^[21] untouchable number,^[12] --> refactorable number.^[25]

373, prime number, balanced prime,^[60] one of the rare primes to be both right and left-truncatable (two-sided prime),^[5] 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 = 2 × 11 × 17, sphenic number,^[11] nontotient, 374⁴ + 1 is prime.^[61]

375 = 3 × 5³, number of regions in regular 11-gon with all diagonals drawn.^[62]

376 = 2³ × 47, pentagonal number,^[27] 1-automorphic number,^[63] nontotient, refactorable number.^[25] There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376 ^[64] It is one of the two three-digit numbers where when squared, the last three digits remain the same.

377 = 13 × 29, Fibonacci number, a centered octahedral number,^[65] a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

378 = 2 × 3³ × 7, triangular number, cake number, hexagonal number,^[16] Smith number.^[7]

379 is a prime number, Chen prime,^[4] lazy caterer number^[22] and a happy number in base 10. It is the sum of the first 15 odd primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53). 379! - 1 is prime.

380 = 2² × 5 × 19, pronic number,^[41] 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.^[66]

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 = 2 × 191, sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Smith number.^[7]

383, prime number, safe prime,^[43] Woodall prime,^[67] 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.^[68] 4³⁸³ - 3³⁸³ is prime.

385 = 5 × 7 × 11, sphenic number,^[11] square pyramidal number,^[69] the number of integer partitions of 18.

385 = 10² + 9² + 8² + 7² + 6² + 5² + 4² + 3² + 2² + 1²

386 = 2 × 193, nontotient, noncototient,^[21] centered heptagonal number,^[3] number of surface points on a cube with edge-length 9.^[70]

387 = 3² × 43, number of graphical partitions of 22.^[71]

388 = 2² × 97 = solution to postage stamp problem with 6 stamps and 6 denominations,^[72] number of uniform rooted trees with 10 nodes.^[73]

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime,^[4] highly cototient number,^[26] strictly non-palindromic number. Smallest conductor of a rank 2 Elliptic curve.

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

${\displaystyle \sum _{n=0}^{10}{390}^{n}}$ is prime^[74]

391 = 17 × 23, Smith number,^[7] centered pentagonal number.^[31]

392 = 2³ × 7², Achilles number.

393 = 3 × 131, Blum integer, Mertens function returns 0.^[33]

394 = 2 × 197 = S₅ a Schröder number,^[75] nontotient, noncototient.^[21]

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.^[76]

396 = 2² × 3² × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number,^[25] Harshad number, digit-reassembly number.

397, prime number, cuban prime,^[29] centered hexagonal number.^[32]

398 = 2 × 199, nontotient.

${\displaystyle \sum _{n=0}^{10}{398}^{n}}$ is prime^[74]

399 = 3 × 7 × 19, sphenic number,^[11] smallest Lucas–Carmichael number, and a Leyland number of the second kind^[77] (${\displaystyle 4^{5}-5^{4}}$). 399! + 1 is prime.