300 (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.<ref>Template:Cite web</ref> It is also a second hexagonal number.<ref>Template:Cite OEIS</ref>

Integers from 301 to 399

310s

316

Template:Main 316 = 2² × 79, a centered triangular number<ref name="A005448">Template:Cite OEIS</ref> and a centered heptagonal number.<ref name="A069099">Template:Cite OEIS</ref>

317

317 is the smallest natural number that does not have its own Wikipedia article, a fact that has itself been noted as making the number notable, creating a situation similar to the interesting number paradox.

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,<ref name=A109611>Template:Cite OEIS</ref> one of the rare primes to be both right and left-truncatable,<ref name=A020994>Template:Cite OEIS</ref> and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.<ref>Guy, Richard; Unsolved Problems in Number Theory, p. 7 Template:ISBN</ref>

319

319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number,<ref name=A006753>Template:Cite OEIS</ref> cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10<ref>Template:Cite OEIS</ref>

320s

320

320 = 2⁶ × 5 = (2⁵) × (2 × 5). 320 is a Leyland number,<ref name=A076980>Template:Cite OEIS</ref> and maximum determinant of a 10 by 10 matrix of zeros and ones.

321

321 = 3 × 107, a Delannoy number<ref>Template:Cite OEIS</ref>

322

322 = 2 × 7 × 23. 322 is a sphenic,<ref name=A007304>Template:Cite OEIS</ref> nontotient, untouchable,<ref name=A005114>Template:Cite OEIS</ref> and a Lucas number.<ref>Template:Cite OEIS</ref> It is also the first unprimeable number to end in 2.

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,<ref>Template:Cite OEIS</ref> and an untouchable number.<ref name=A005114 />

326

326 = 2 × 163. 326 is a nontotient, noncototient,<ref name=A005278>Template:Cite OEIS</ref> and an untouchable number.<ref name=A005114 /> 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<ref name=A000124>Template:Cite OEIS</ref>

327

327 = 3 × 109. 327 is a perfect totient number,<ref>Template:Cite OEIS</ref> number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing<ref>Template:Cite OEIS</ref>

328

328 = 2³ × 41. 328 is a refactorable number,<ref name=A033950>Template:Cite OEIS</ref> 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.<ref name=A100827>Template:Cite OEIS</ref>

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 <math>\tbinom {11}4 </math>), a pentagonal number,<ref name=A000326>Template:Cite OEIS</ref> divisible by the number of primes below it, and a sparsely totient number.<ref>Template:Cite OEIS</ref>

331

331 is a prime number, super-prime, cuban prime,<ref name=A002407>Template:Cite OEIS</ref> a lucky prime,<ref name=A031157>Template:Cite OEIS</ref> sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,<ref name=A005891>Template:Cite OEIS</ref> centered hexagonal number,<ref name=A003215>Template:Cite OEIS</ref> and Mertens function returns 0.<ref name=A028442>Template:Cite OEIS</ref>

332

332 = 2² × 83, Mertens function returns 0.<ref name=A028442/>

333

333 = 3² × 37, Mertens function returns 0;<ref name=A028442/> repdigit; 2³³³ is the smallest power of two greater than a googol.

334

334 = 2 × 167, nontotient.<ref>Template:Cite OEIS</ref>

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,<ref name=A005114/> number of partitions of 41 into prime parts,<ref>Template:Cite OEIS</ref> largely composite number.<ref name="OEIS-A067128">Template:Cite OEIS</ref>

337

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,<ref name=A109611>Template:Cite OEIS</ref> star number

338

338 = 2 × 13², nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.<ref>Template:Cite OEIS</ref>

339

339 = 3 × 113, Ulam number<ref>Template:Cite OEIS</ref>

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.<ref name=A005278/> 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.

342

342 = 2 × 3² × 19, pronic number,<ref name=A002378>Template:Cite OEIS</ref> Untouchable number.<ref name=A005114/>

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,<ref>Template:Cite OEIS</ref> noncototient,<ref name=A005278/> totient sum of the first 33 integers, refactorable number.<ref name=A033950/>

345

345 = 3 × 5 × 23, sphenic number,<ref name=A007304/> idoneal number

346

346 = 2 × 173, Smith number,<ref name=A006753/> noncototient.<ref name=A005278/>

347

347 is a prime number, emirp, safe prime,<ref name=A005385>Template:Cite OEIS</ref> Eisenstein prime with no imaginary part, Chen prime,<ref name=A109611/> 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.<ref name=A033950/>

349

349, prime number, twin prime, lucky prime, sum of three consecutive primes (109 + 113 + 127), 5³⁴⁹ - 4³⁴⁹ is a prime number.<ref>Template:Cite OEIS</ref>

350s

350

350 = 2 × 5² × 7 = <math>\left\{ {7 \atop 4} \right\}</math>, primitive semiperfect number,<ref>Template:Cite OEIS</ref> 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,<ref>Template:Cite web</ref> sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence<ref>Template:Cite OEIS</ref> and number of compositions of 15 into distinct parts.<ref>Template:Cite OEIS</ref>

• The international calling code for Portugal

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<ref name=A000124/>

• The international calling code for Luxembourg

353

• The international calling code for Republic of Ireland

354

354 = 2 × 3 × 59 = 1⁴ + 2⁴ + 3⁴ + 4⁴,<ref>Template:Cite OEIS</ref><ref>Template:Cite OEIS</ref> sphenic number,<ref name=A007304/> nontotient, also SMTP code meaning start of mail input. It is also sum of absolute value of the coefficients of Conway's polynomial.

• The international calling code for Iceland

355

355 = 5 × 71, Smith number,<ref name=A006753/> Mertens function returns 0,<ref name=A028442/> divisible by the number of primes below it.<ref>Template:Cite web</ref> The cototient of 355 is 75,<ref>Template:Cite web</ref> 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.<ref name=A028442/>

357

357 = 3 × 7 × 17, sphenic number.<ref name=A007304/>

358

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,<ref name=A028442/> number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.<ref>Template:Cite OEIS</ref>

• The international calling code for Finland

360s

361

361 = 19². 361 is a centered triangular number,<ref name=A005448>Template:Cite OEIS</ref> centered octagonal number, centered decagonal number,<ref>Template:Cite OEIS</ref> member of the Mian–Chowla sequence;<ref>Template:Cite OEIS</ref> 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,<ref>Template:Cite OEIS</ref> Mertens function returns 0,<ref name=A028442/> nontotient, noncototient.<ref name=A005278/>

364

364 = 2² × 7 × 13, tetrahedral number,<ref name =A000292>Template:Cite OEIS</ref> sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,<ref name=A028442/> 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.<ref name =A000292/>

366

366 = 2 × 3 × 61, sphenic number,<ref name=A007304/> Mertens function returns 0,<ref name=A028442/> noncototient,<ref name=A005278/> number of complete partitions of 20,<ref>Template:Cite OEIS</ref> 26-gonal and 123-gonal. Also the number of days in a leap year.

367

367 is a prime number, a lucky prime,<ref name=A031157/> Perrin number,<ref>Template:Cite OEIS</ref> happy number, prime index prime and a strictly non-palindromic number.

368

368 = 2⁴ × 23. It is also a Leyland number.<ref name=A076980/>

370s

370

370 = 2 × 5 × 37, sphenic number,<ref name=A007304/> 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,<ref>Template:Cite OEIS</ref> 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,<ref name=A005278/> untouchable number,<ref name=A005114/> --> refactorable number.<ref name=A033950/>

373

373, prime number, balanced prime,<ref>Template:Cite OEIS</ref> one of the rare primes to be both right and left-truncatable (two-sided prime),<ref name=A020994>Template:Cite OEIS</ref> 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,<ref name=A007304/> nontotient, 374⁴ + 1 is prime.<ref>Template:Cite OEIS</ref>

375

375 = 3 × 5³, number of regions in regular 11-gon with all diagonals drawn.<ref>Template:Cite OEIS</ref>

376

376 = 2³ × 47, pentagonal number,<ref name=A000326/> 1-automorphic number,<ref>Template:Cite OEIS</ref> nontotient, refactorable number.<ref name=A033950/>

378

378 = 2 × 3³ × 7, 27th triangular number,<ref>Template:Cite web</ref> cake number,<ref>Template:Cite web</ref> hexagonal number,<ref name=A000384>Template:Cite OEIS</ref> Smith number.<ref name=A006753/>

379

379 is a prime number, Chen prime,<ref name=A109611/> lazy caterer number<ref name=A000124/> 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,<ref name=A002378/> 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.<ref>Template:Cite OEIS</ref>

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.<ref name=A006753/>

383

383, prime number, safe prime,<ref name=A005385/> Woodall prime,<ref>Template:Cite OEIS</ref> 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.<ref>Template:Cite OEIS</ref> 4³⁸³ - 3³⁸³ is prime.

385

385 = 5 × 7 × 11, sphenic number,<ref name=A007304/> square pyramidal number,<ref>Template:Cite OEIS</ref> the number of integer partitions of 18.

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

386

386 = 2 × 193, nontotient, noncototient,<ref name=A005278/> centered heptagonal number,<ref name=A069099>Template:Cite OEIS</ref> number of surface points on a cube with edge-length 9.<ref>Template:Cite OEIS</ref>

387

387 = 3² × 43, number of graphical partitions of 22.<ref>Template:Cite OEIS</ref>

388

388 = 2² × 97 = solution to postage stamp problem with 6 stamps and 6 denominations,<ref>Template:Cite OEIS</ref> number of uniform rooted trees with 10 nodes.<ref>Template:Cite OEIS</ref>

389

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime,<ref name=A109611/> highly cototient number,<ref name=A100827/> 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,

<math>\sum_{n=0}^{10}{390}^{n}</math> is prime<ref name=A162862>Template:Cite OEIS</ref>

391

391 = 17 × 23, Smith number,<ref name=A006753/> centered pentagonal number.<ref name=A005891/>

392

392 = 2³ × 7², Achilles number.

393

393 = 3 × 131, Blum integer, Mertens function returns 0.<ref name=A028442/>

394

394 = 2 × 197 = S₅ a Schröder number,<ref>Template:Cite OEIS</ref> nontotient, noncototient.<ref name=A005278/>

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.<ref>Template:Cite OEIS</ref>

396

396 = 2² × 3² × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number,<ref name=A033950/> Harshad number, digit-reassembly number.

397

397, prime number, cuban prime,<ref name=A002407/> centered hexagonal number.<ref name=A003215/>

398

398 = 2 × 199, nontotient.

<math>\sum_{n=0}^{10}{398}^{n}</math> is prime<ref name=A162862/>

399

399 = 3 × 7 × 19, sphenic number,<ref name=A007304/> smallest Lucas–Carmichael number, and a Leyland number of the second kind<ref>Template:Cite OEIS</ref> Template:No wrap 399! + 1 is prime.