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 and the 24th triangular number.^[1]

315 = 3² × 5 × 7 = ${\displaystyle D_{7,3}\!}$, rencontres number, highly composite odd number, having 12 divisors.^[2]

316 = 2² × 79, a centered triangular number^[3] and a centered heptagonal number.^[4]

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,^[5] one of the rare primes to be both right and left-truncatable,^[6] and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.^[7]

319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number,^[8] cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10^[9]

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

321 = 3 × 107, a Delannoy number^[11]

322 = 2 × 7 × 23. 322 is a sphenic,^[12] nontotient, untouchable,^[13] and a Lucas number.^[14] 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.^[15] 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,^[16] and an untouchable number.^[13]

326 = 2 × 163. 326 is a nontotient, noncototient,^[17] and an untouchable number.^[13] 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^[18]

327 = 3 × 109. 327 is a perfect totient number,^[19] number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing^[20]

328 = 2³ × 41. 328 is a refactorable number,^[21] 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.^[22]

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,^[23] divisible by the number of primes below it, and a sparsely totient number.^[24]

331 is a prime number, super-prime, cuban prime,^[25] a lucky prime,^[26] sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,^[27] centered hexagonal number,^[28] and Mertens function returns 0.^[29]

332 = 2² × 83, Mertens function returns 0.^[29]

333 = 3² × 37, Mertens function returns 0;^[29] repdigit; 2³³³ is the smallest power of two greater than a googol.

334 = 2 × 167, nontotient.^[30]

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,^[13] number of partitions of 41 into prime parts,^[31] largely composite number.^[32]

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,^[5] star number

338 = 2 × 13², nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.^[33]

339 = 3 × 113, Ulam number^[34]

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.^[17] 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,^[35] centered cube number,^[36] 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,^[37] Untouchable number.^[13]

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,^[38] noncototient,^[17] totient sum of the first 33 integers, refactorable number.^[21]

345 = 3 × 5 × 23, sphenic number,^[12] idoneal number

346 = 2 × 173, Smith number,^[8] noncototient.^[17]

347 is a prime number, emirp, safe prime,^[39] Eisenstein prime with no imaginary part, Chen prime,^[5] 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.^[21]

349, prime number, twin prime, lucky prime, sum of three consecutive primes (109 + 113 + 127), 5³⁴⁹ - 4³⁴⁹ is a prime number.^[40]

350 = 2 × 5² × 7 = ${\displaystyle \left\{{7 \atop 4}\right\}}$, primitive semiperfect number,^[41] 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, 26th triangular number,^[42] sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence^[43] and number of compositions of 15 into distinct parts.^[44]

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^[18]

354 = 2 × 3 × 59 = 1⁴ + 2⁴ + 3⁴ + 4⁴,^[45][46] sphenic number,^[12] 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,^[8] Mertens function returns 0,^[29] divisible by the number of primes below it.^[47] The cototient of 355 is 75,^[48] 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.^[29]

357 = 3 × 7 × 17, sphenic number.^[12]

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,^[29] number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.^[49]

361 = 19². 361 is a centered triangular number,^[3] centered octagonal number, centered decagonal number,^[50] member of the Mian–Chowla sequence;^[51] 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,^[52] Mertens function returns 0,^[29] nontotient, noncototient.^[17]

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

366 = 2 × 3 × 61, sphenic number,^[12] Mertens function returns 0,^[29] noncototient,^[17] number of complete partitions of 20,^[54] 26-gonal and 123-gonal. Also the number of days in a leap year.

367 is a prime number, a lucky prime,^[26] Perrin number,^[55] happy number, prime index prime and a strictly non-palindromic number.

368 = 2⁴ × 23. It is also a Leyland number.^[10]

370 = 2 × 5 × 37, sphenic number,^[12] 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,^[56] 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,^[17] untouchable number,^[13] --> refactorable number.^[21]

373, prime number, balanced prime,^[57] one of the rare primes to be both right and left-truncatable (two-sided prime),^[6] 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,^[12] nontotient, 374⁴ + 1 is prime.^[58]

375 = 3 × 5³, number of regions in regular 11-gon with all diagonals drawn.^[59]

376 = 2³ × 47, pentagonal number,^[23] 1-automorphic number,^[60] nontotient, refactorable number.^[21] There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376 ^[61] 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,^[62] a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

378 = 2 × 3³ × 7, 27th triangular number,^[63] cake number,^[64] hexagonal number,^[65] Smith number.^[8]

379 is a prime number, Chen prime,^[5] lazy caterer number^[18] 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,^[37] 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.^[8]

383, prime number, safe prime,^[39] 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,^[12] 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,^[17] centered heptagonal number,^[4] 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,^[5] highly cototient number,^[22] 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,^[8] centered pentagonal number.^[27]

392 = 2³ × 7², Achilles number.

393 = 3 × 131, Blum integer, Mertens function returns 0.^[29]

394 = 2 × 197 = S₅ a Schröder number,^[75] nontotient, noncototient.^[17]

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,^[21] Harshad number, digit-reassembly number.

397, prime number, cuban prime,^[25] centered hexagonal number.^[28]

398 = 2 × 199, nontotient.

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

399 = 3 × 7 × 19, sphenic number,^[12] smallest Lucas–Carmichael number, and a Leyland number of the second kind^[77] (${\displaystyle 4^{5}-5^{4}}$). 399! + 1 is prime.