Number 300

The number 300 is a triangular number and the sum of a pair of twin primes (149 + 151), as well as the sum of ten consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). It is palindromic in 3 consecutive bases: 300₁₀ = 606₇ = 454₈ = 363₉, and also in base 13. Factorization is 2² × 3 × 5². 300⁶⁴ + 1 is prime

300s

301

302

303

304

305

306

307

308

309

309 = 3 × 103, Blum integer, number of primes <= 2¹¹. As of April 2024^[update], it is the lowest number to not have an article in Wikipedia, possibly making it interesting in the interesting number paradox.

310s

310

311

312

312 = 2³ × 3 × 13, idoneal number.

313

314

314 = 2 × 157. 314 is a nontotient, smallest composite number in Somos-4 sequence.

315

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

316

316 = 2² × 79, a centered triangular number and a centered heptagonal number.

317

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

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

318

319

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

320s

320

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

321

321 = 3 × 107, a Delannoy number

322

322 = 2 × 7 × 23. 322 is a sphenic, nontotient, untouchable, and a Lucas number.

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. 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, and an untouchable number.

325

325 = 5² × 13. 325 is a triangular number, hexagonal number, nonagonal number, centered nonagonal number. 325 is the smallest number to be the sum of two squares in 3 different ways: 1² + 18², 6² + 17² and 10² + 15². 325 is also the smallest (and only known) 3-hyperperfect number.

326

326 = 2 × 163. 326 is a nontotient, noncototient, and an untouchable number. 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

327

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

328

328 = 2³ × 41. 328 is a refactorable number, 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.

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 ${\displaystyle {\tbinom {11}{4}}}$ ), a pentagonal number, divisible by the number of primes below it, and a sparsely totient number.

331

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

332

332 = 2² × 83, Mertens function returns 0.

333

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

334

334 = 2 × 167, nontotient.

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, number of partitions of 41 into prime parts.

337

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

338

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

339

339 = 3 × 113, Ulam number

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. 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, centered cube number, 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

342 = 2 × 3² × 19, pronic number, Untouchable number.

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, noncototient, totient sum of the first 33 integers, refactorable number.

345

345 = 3 × 5 × 23, sphenic number, idoneal number

346

346 = 2 × 173, Smith number, noncototient.

347

347 is a prime number, emirp, safe prime, Eisenstein prime with no imaginary part, Chen prime, 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.

349

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

350s

350

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

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

353

354

354 = 2 × 3 × 59 = 1⁴ + 2⁴ + 3⁴ + 4⁴, sphenic number, 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, Mertens function returns 0, divisible by the number of primes below it.

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.

356

356 = 2² × 89, Mertens function returns 0.

357

357 = 3 × 7 × 17, sphenic number.

358

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

359

360s

360

361

361 = 19², centered triangular number, centered octagonal number, centered decagonal number, member of the Mian–Chowla sequence; 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, Mertens function returns 0, nontotient, noncototient.

363

364

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

365

366

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

367

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

368

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

369

370s

370

370 = 2 × 5 × 37, sphenic number, 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, 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, untouchable number, --> refactorable number.

373

373, prime number, balanced prime, one of the rare primes to be both right and left-truncatable (two-sided prime), sum of five consecutive primes (67 + 71 + 73 + 79 + 83), permutable prime with 337 and 733, palindromic prime in 3 consecutive bases: 565₈ = 454₉ = 373₁₀ and also in base 4: 11311₄. Also a sexy prime with 367 and 379.

374

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

375

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

376

376 = 2³ × 47, pentagonal number, 1-automorphic number, nontotient, refactorable number. There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376

377

377 = 13 × 29, Fibonacci number, a centered octahedral number, a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

378

378 = 2 × 3³ × 7, triangular number, cake number, hexagonal number, Smith number.

379

379 is a prime number, Chen prime, lazy caterer number and a happy number in base 10. It is the sum of the 15 consecutive 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, 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.

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.

383

383, prime number, safe prime, Woodall prime, 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. 4³⁸³ - 3³⁸³ is prime.

384

385

385 = 5 × 7 × 11, sphenic number, square pyramidal number, the number of integer partitions of 18.

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

386

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

387

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

388

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

389

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime, highly cototient number, 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,

${\displaystyle \sum _{n=0}^{10}{390}^{n}}$  is prime

391

391 = 17 × 23, Smith number, centered pentagonal number.

392

392 = 2³ × 7², Achilles number.

393

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

394

394 = 2 × 197 = S₅ a Schröder number, nontotient, noncototient.

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.

396

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

397

397, prime number, cuban prime, centered hexagonal number.

398

398 = 2 × 199, nontotient.

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

399

399 = 3 × 7 × 19, sphenic number, smallest Lucas–Carmichael number, Leyland number of the second kind. 399! + 1 is prime.