300 (number)

Last updated
299 300 301
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.

Contents

In Mathematics

300 is a composite number and the 24th triangular number. [1]

Integers from 301 to 399

300s

301

302

303

304

305

306

307

308

309

310s

310

311

312

313

314

315

315 = 32× 5 × 7 = , rencontres number, highly composite odd number, having 12 divisors. [2]

316

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

317

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]

318

319

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]

320s

320

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

321 = 3 × 107, a Delannoy number [11]

322

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

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

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]

325

326

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

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

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

329 = 7 × 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number. [22]

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

331

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

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

333

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

334

334 = 2 × 167, nontotient. [30]

335

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

336

336 = 24× 3 × 7, untouchable number, [13] number of partitions of 41 into prime parts, [31] largely composite number. [32]

337

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

338

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

339

339 = 3 × 113, Ulam number [34]

340s

340

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

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 leastcompositeodd modulus m greater than the base b, that satisfies the Fermat property "bm1  1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.

342

342 = 2 × 32× 19, pronic number, [37] Untouchable number. [13]

343

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

344 = 23× 43, octahedral number, [38] noncototient, [17] totient sum of the first 33 integers, refactorable number. [21]

345

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

346

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

347

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

348 = 22× 3 × 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number. [21]

349

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

350s

350

350 = 2 × 52× 7 = , 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

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

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]

353

354

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

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

356 = 22× 89, Mertens function returns 0. [29]

357

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

358

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]

359

360s

360

361

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

362 = 2 × 181 = σ2(19): sum of squares of divisors of 19, [52] Mertens function returns 0, [29] nontotient, noncototient. [17]

363

364

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]

365

366

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

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

368

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

369

370s

370

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

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

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

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

374 = 2 × 11 × 17, sphenic number, [12] nontotient, 3744 + 1 is prime. [58]

375

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

376

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

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

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

379

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.

380s

380

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

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. [8]

383

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.

384

385

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

386 = 2 × 193, nontotient, noncototient, [17] centered heptagonal number, [4] number of surface points on a cube with edge-length 9. [70]

387

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

388

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

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.

390s

390

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

is prime [74]

391

391 = 17 × 23, Smith number, [8] centered pentagonal number. [27]

392

392 = 23× 72, Achilles number.

393

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

394

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

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. [76]

396

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

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

398

398 = 2 × 199, nontotient.

is prime [74]

399

399 = 3 × 7 × 19, sphenic number, [12] smallest Lucas–Carmichael number, and a Leyland number of the second kind [77] (). 399! + 1 is prime.

Related Research Articles

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or six dozen.

86 (eighty-six) is the natural number following 85 and preceding 87.

34 (thirty-four) is the natural number following 33 and preceding 35.

58 (fifty-eight) is the natural number following 57 and preceding 59.

114 is the natural number following 113 and preceding 115.

100 or one hundred is the natural number following 99 and preceding 101.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

<span class="mw-page-title-main">360 (number)</span> Natural number

360 is the natural number following 359 and preceding 361.

400 is the natural number following 399 and preceding 401.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10, it is a Harshad number. It is also the first number to be the square of a sphenic number.

2000 is a natural number following 1999 and preceding 2001.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

230 is the natural number following 229 and preceding 231.

240 is the natural number following 239 and preceding 241.

318 is the natural number following 317 and preceding 319.

308 is the natural number following 307 and preceding 309.

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  69. Sloane, N. J. A. (ed.). "SequenceA000330(Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  70. Sloane, N. J. A. (ed.). "SequenceA005897(a(n) = 6*n^2 + 2 for n > 0, a(0)=1)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  71. Sloane, N. J. A. (ed.). "SequenceA000569(Number of graphical partitions of 2n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  72. Sloane, N. J. A. (ed.). "SequenceA084192(Array read by antidiagonals: T(n,k) = solution to postage stamp problem with n stamps and k denominations (n >= 1, k >= 1))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  73. Sloane, N. J. A. (ed.). "SequenceA317712(Number of uniform rooted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  74. 1 2 Sloane, N. J. A. (ed.). "SequenceA162862(Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  75. Sloane, N. J. A. (ed.). "SequenceA006318(Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  76. Sloane, N. J. A. (ed.). "SequenceA002955(Number of (unordered, unlabeled) rooted trimmed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  77. Sloane, N. J. A. (ed.). "SequenceA045575(Leyland numbers of the second kind)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.