300 (number)

Last updated
299 300 301
Cardinal three hundred
Ordinal 300th
(three hundredth)
Factorization 22 × 3 × 52
Greek numeral Τ´
Roman numeral CCC, 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

342

342 = 2 × 32× 19, pronic number, [35] 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, [36] 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, [37] 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. [38]

350s

350

350 = 2 × 52× 7 = , primitive semiperfect number, [39] 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, [40] sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence [41] and number of compositions of 15 into distinct parts. [42]

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, [43] [44] 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. [45] The cototient of 355 is 75, [46] 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. [47]

359

360s

360

361

361 = 192. 361 is a centered triangular number, [3] centered octagonal number, centered decagonal number, [48] member of the Mian–Chowla sequence; [49] 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, [50] Mertens function returns 0, [29] nontotient, noncototient. [17]

363

364

364 = 22× 7 × 13, tetrahedral number, [51] 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. [51]

365

366

366 = 2 × 3 × 61, sphenic number, [12] Mertens function returns 0, [29] noncototient, [17] number of complete partitions of 20, [52] 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, [53] 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, [54] 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, [55] 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. [56]

375

375 = 3 × 53, number of regions in regular 11-gon with all diagonals drawn. [57]

376

376 = 23× 47, pentagonal number, [23] 1-automorphic number, [58] 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 [59] 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, [60] a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

378

378 = 2 × 33× 7, 27th triangular number, [61] cake number, [62] hexagonal number, [63] 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, [35] 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. [64]

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, [37] Woodall prime, [65] 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. [66] 4383 - 3383 is prime.

384

385

385 = 5 × 7 × 11, sphenic number, [12] square pyramidal number, [67] 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. [68]

387

387 = 32× 43, number of graphical partitions of 22. [69]

388

388 = 22× 97 = solution to postage stamp problem with 6 stamps and 6 denominations, [70] number of uniform rooted trees with 10 nodes. [71]

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 [72]

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, [73] 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. [74]

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 [72]

399

399 = 3 × 7 × 19, sphenic number, [12] smallest Lucas–Carmichael number, and a Leyland number of the second kind [75] (). 399! + 1 is prime.

References

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  66. Sloane, N. J. A. (ed.). "SequenceA072385(Primes which can be represented as the sum of a prime and its reverse)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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  75. Sloane, N. J. A. (ed.). "SequenceA045575(Leyland numbers of the second kind)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.