300 (number)

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Template:More citations needed Template:Infobox number

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

In Mathematics

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

Integers from 301 to 399

300s

301

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302

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303

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304

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305

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306

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307

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308

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309

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310s

310

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311

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312

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313

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314

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315

315 = 32 × 5 × 7 = D7,3, rencontres number, highly composite odd number, having 12 divisors.[2]

It is a Harshad number, as it is divisible by the sum of its digits.[3]

It is a Zuckerman number, as it is divisible by the product of its digits.[4]

316

316 = 22 × 79, a centered triangular number[5] and a centered heptagonal number.[6]

317

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,[7] one of the rare primes to be both right and left-truncatable,[8] and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.[9]

318

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319

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

320s

320

320 = 26 × 5 = (25) × (2 × 5). 320 is a Leyland number,[12] and maximum determinant of a 10 by 10 matrix of zeros and ones.

321

321 = 3 × 107, a Delannoy number[13]

322

322 = 2 × 7 × 23. 322 is a sphenic,[14] nontotient, untouchable,[15] and a Lucas number.[16] 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.[17] 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,[18] and an untouchable number.[15]

325

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326

326 = 2 × 163. 326 is a nontotient, noncototient,[19] and an untouchable number.[15] 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[20]

327

327 = 3 × 109. 327 is a perfect totient number,[21] number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing[22]

328

328 = 23 × 41. 328 is a refactorable number,[23] 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.[24]

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 (114)), a pentagonal number,[25] divisible by the number of primes below it, and a sparsely totient number.[26]

331

331 is a prime number, super-prime, cuban prime,[27] a lucky prime,[28] sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,[29] centered hexagonal number,[30] and Mertens function returns 0.[31]

332

332 = 22 × 83, Mertens function returns 0.[31]

333

333 = 32 × 37, Mertens function returns 0;[31] repdigit; 2333 is the smallest power of two greater than a googol.

334

334 = 2 × 167, nontotient.[32]

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,[15] number of partitions of 41 into prime parts,[33] largely composite number.[34]

337

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,[7] star number

338

338 = 2 × 132, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.[35]

339

339 = 3 × 113, Ulam number[36]

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.[19] 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 Template:OEIS and Template:OEIS.

341

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342

342 = 2 × 32 × 19, pronic number,[37] Untouchable number.[15]

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,[19] totient sum of the first 33 integers, refactorable number.[23]

345

345 = 3 × 5 × 23, sphenic number,[14] idoneal number

346

346 = 2 × 173, Smith number,[10] noncototient.[19]

347

347 is a prime number, emirp, safe prime,[39] Eisenstein prime with no imaginary part, Chen prime,[7] 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.[23]

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 = {74}, 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[20]

353

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354

354 = 2 × 3 × 59 = 14 + 24 + 34 + 44,[45][46] sphenic number,[14] 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,[10] Mertens function returns 0,[31] 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.[31]

357

357 = 3 × 7 × 17, sphenic number.[14]

358

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,[31] number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.[49]

359

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360s

360

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361

361 = 192. 361 is a centered triangular number,[5] 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,[31] nontotient, noncototient.[19]

363

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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,[31] 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

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366

366 = 2 × 3 × 61, sphenic number,[14] Mertens function returns 0,[31] noncototient,[19] 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,[28] Perrin number,[55] happy number, prime index prime and a strictly non-palindromic number.

368

368 = 24 × 23. It is also a Leyland number.[12]

369

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370s

370

370 = 2 × 5 × 37, sphenic number,[14] 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,[19] untouchable number,[15] --> refactorable number.[23]

373

373, prime number, balanced prime,[57] one of the rare primes to be both right and left-truncatable (two-sided prime),[8] 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,[14] 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,[25] 1-automorphic number,[60] nontotient, refactorable number.[23] 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.[10]

379

379 is a prime number, Chen prime,[7] lazy caterer number[20] 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.[10]

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

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385

385 = 5 × 7 × 11, sphenic number,[14] 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,[19] centered heptagonal number,[6] 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,[7] highly cototient number,[24] 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,

∑n=010390n is prime[74]

391

391 = 17 × 23, Smith number,[10] centered pentagonal number.[29]

392

392 = 23 × 72, Achilles number.

393

393 = 3 × 131, Blum integer, Mertens function returns 0.[31]

394

394 = 2 × 197 = S5 a Schröder number,[75] nontotient, noncototient.[19]

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,[23] Harshad number, digit-reassembly number.

397

397, prime number, cuban prime,[27] centered hexagonal number.[30]

398

398 = 2 × 199, nontotient.

∑n=010398n is prime[74]

399

399 = 3 × 7 × 19, sphenic number,[14] smallest Lucas–Carmichael number, and a Leyland number of the second kind[77] Template:No wrap 399! + 1 is prime.

References

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  1. ↑ Template:Cite web
  2. ↑ Template:Cite OEIS
  3. ↑ Template:Cite OEIS
  4. ↑ Template:Cite OEIS
  5. ↑ 5.0 5.1 Template:Cite OEIS
  6. ↑ 6.0 6.1 Template:Cite OEIS
  7. ↑ 7.0 7.1 7.2 7.3 7.4 Template:Cite OEIS
  8. ↑ 8.0 8.1 Template:Cite OEIS
  9. ↑ Guy, Richard; Unsolved Problems in Number Theory, p. 7 Template:ISBN
  10. ↑ 10.0 10.1 10.2 10.3 10.4 10.5 Template:Cite OEIS
  11. ↑ Template:Cite OEIS
  12. ↑ 12.0 12.1 Template:Cite OEIS
  13. ↑ Template:Cite OEIS
  14. ↑ 14.0 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 Template:Cite OEIS
  15. ↑ 15.0 15.1 15.2 15.3 15.4 15.5 Template:Cite OEIS
  16. ↑ Template:Cite OEIS
  17. ↑ Template:Cite OEIS
  18. ↑ Template:Cite OEIS
  19. ↑ 19.0 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 Template:Cite OEIS
  20. ↑ 20.0 20.1 20.2 Template:Cite OEIS
  21. ↑ Template:Cite OEIS
  22. ↑ Template:Cite OEIS
  23. ↑ 23.0 23.1 23.2 23.3 23.4 23.5 Template:Cite OEIS
  24. ↑ 24.0 24.1 Template:Cite OEIS
  25. ↑ 25.0 25.1 Template:Cite OEIS
  26. ↑ Template:Cite OEIS
  27. ↑ 27.0 27.1 Template:Cite OEIS
  28. ↑ 28.0 28.1 Template:Cite OEIS
  29. ↑ 29.0 29.1 Template:Cite OEIS
  30. ↑ 30.0 30.1 Template:Cite OEIS
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  66. ↑ Template:Cite OEIS
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  70. ↑ Template:Cite OEIS
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  73. ↑ Template:Cite OEIS
  74. ↑ 74.0 74.1 Template:Cite OEIS
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  76. ↑ Template:Cite OEIS
  77. ↑ Template:Cite OEIS
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