# 300 (number)

Short description: Natural number
 ← 299 300 301 →
Cardinalthree hundred
Ordinal300th
(three hundredth)
Factorization22 × 3 × 52
Greek numeralΤ´
Roman numeralCCC
Binary1001011002
Ternary1020103
Quaternary102304
Quinary22005
Senary12206
Octal4548
Duodecimal21012
VigesimalF020
Base 368C36
Hebrewש (Shin)

300 (three hundred) is the natural number following 299 and preceding 301.

## Mathematical properties

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

## Integers from 301 to 399

### 300s

#### 301

Main page: 301 (number)

#### 302

Main page: 302 (number)

#### 303

Main page: 303 (number)

#### 304

Main page: 304 (number)

#### 305

Main page: 305 (number)

#### 306

Main page: 306 (number)

#### 307

Main page: 307 (number)

#### 308

308 = 22 × 7 × 11. 308 is a nontotient,[1] totient sum of the first 31 integers, heptagonal pyramidal number,[2] and the sum of two consecutive primes (151 + 157).

#### 309

309 = 3 × 103, Blum integer, number of primes <= 211.[3]

### 310s

#### 310

Main page: 310 (number)

#### 311

Main page: 311 (number)

#### 312

Main page: 312 (number)

312 = 23 × 3 × 13, idoneal number.

#### 313

Main page: 313 (number)

#### 314

314 = 2 × 157. 314 is a nontotient,[1] smallest composite number in Somos-4 sequence.[4]

#### 315

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

#### 316

316 = 22 × 79, a centered triangular number[6] and a centered heptagonal number.[7]

#### 317

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,[8] and a strictly non-palindromic number.

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

#### 318

Main page: 318 (number)

#### 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,[citation needed] and a Lucas number.[15]

#### 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.[16] 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,[17] and an untouchable number.[citation needed]

#### 325

325 = 52 × 13. 325 is a triangular number, hexagonal number,[18] nonagonal number,[19] centered nonagonal number.[20] 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,[21] and an untouchable number.[citation needed] 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 (sequence A000124 in the OEIS).

#### 327

327 = 3 × 109. 327 is a perfect totient number,[22] number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing[23]

#### 328

328 = 23 × 41. 328 is a refactorable number,[24] 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.[25]

### 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,[26] divisible by the number of primes below it, and a sparsely totient number.[27]

#### 331

331 is a prime number, super-prime, cuban 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]

#### 334

334 = 2 × 167, nontotient.[32]

#### 335

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

#### 336

336 = 24 × 3 × 7, untouchable number,[citation needed] number of partitions of 41 into prime parts.[33]

#### 337

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,[8] star number

#### 338

338 = 2 × 132, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.[34]

#### 339

339 = 3 × 113, Ulam number[35]

### 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.[21] 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,[36] centered cube number,[37] 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 "bm−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,[38] Untouchable number.[citation needed]

#### 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,[39] noncototient,[21] totient sum of the first 33 integers, refactorable number.[24]

#### 345

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

#### 346

346 = 2 × 173, Smith number,[10] noncototient.[21]

#### 347

347 is a prime number, emirp, safe prime,[40] Eisenstein prime with no imaginary part, Chen prime,[8] Friedman prime since 347 = 73 + 4, and a strictly non-palindromic number.

#### 348

348 = 22 × 3 × 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.[24]

#### 349

349, prime number, sum of three consecutive primes (109 + 113 + 127), 5349 - 4349 is a prime number.[41]

### 350s

#### 350

350 = 2 × 52 × 7 = $\displaystyle{ \left\{ {7 \atop 4} \right\} }$, primitive semiperfect number,[42] 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[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 (sequence A000124 in the OEIS).

#### 353

Main page: 353 (number)

#### 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.

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.[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.[47]

#### 359

Main page: 359 (number)

### 360s

#### 360

Main page: 360 (number)

#### 361

361 = 192, centered triangular number,[6] 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,[31] nontotient, noncototient.[21]

#### 363

Main page: 363 (number)

#### 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,[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.[52]

#### 365

Main page: 365 (number)

#### 366

366 = 2 × 3 × 61, sphenic number,[14] Mertens function returns 0,[31] noncototient,[21] number of complete partitions of 20,[53] 26-gonal and 123-gonal. Also the number of days in a leap year.

#### 367

367 is a prime number, Perrin number,[54] happy number, prime index prime and a strictly non-palindromic number.

#### 368

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

#### 369

Main page: 369 (number)

### 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 (sequence A055233 in the OEIS), 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,[21] untouchable number,[citation needed] refactorable number.[24]

#### 373

373, prime number, balanced prime,[55] 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.

#### 374

374 = 2 × 11 × 17, sphenic number,[14] 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,[26] 1-automorphic number,[58] nontotient, refactorable number.[24] There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376 [59]

#### 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, triangular number, cake number, hexagonal number,[18] Smith number.[10]

#### 379

379 is a prime number, Chen prime,[8] lazy caterer number (sequence A000124 in the OEIS) 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.[38]

#### 381

381 = 3 × 127, palindromic in base 2 and base 8.

It 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,[40] Woodall prime,[61] 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.[62] 4383 - 3383 is prime.

#### 384

Main page: 384 (number)

#### 385

385 = 5 × 7 × 11, sphenic number,[14] square pyramidal number,[63] the number of integer partitions of 18.

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

#### 386

386 = 2 × 193, nontotient, noncototient,[21] centered heptagonal number,[7] number of surface points on a cube with edge-length 9.[64]

#### 387

387 = 32 × 43, number of graphical partitions of 22.[65]

#### 388

388 = 22 × 97 = solution to postage stamp problem with 6 stamps and 6 denominations,[66] number of uniform rooted trees with 10 nodes.[67]

#### 389

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime,[8] highly cototient number,[25] 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[68]

#### 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,[69] nontotient, noncototient.[21]

#### 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.[70]

#### 396

396 = 22 × 32 × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number,[24] Harshad number, digit-reassembly number.

#### 397

397, prime number, cuban prime,[28] centered hexagonal number.[30]

#### 398

398 = 2 × 199, nontotient.

$\displaystyle{ \sum_{n=0}^{10}{398}^{n} }$ is prime[68]

#### 399

399 = 3 × 7 × 19, sphenic number,[14] smallest Lucas–Carmichael number, Leyland number of the second kind. 399! + 1 is prime.

## References

1. Sloane, N. J. A., ed. "Sequence A005277". OEIS Foundation.
2. Sloane, N. J. A., ed. "Sequence A002413 (Heptagonal pyramidal numbers)". OEIS Foundation. Retrieved 2016-05-22.
3. Sloane, N. J. A., ed. "Sequence A007053 (Number of primes <= 2^n)". OEIS Foundation. Retrieved 2022-06-02.
4. Sloane, N. J. A., ed. "Sequence A006720 (Somos-4 sequence)". OEIS Foundation.
5. Sloane, N. J. A., ed. "Sequence A005448 (Centered triangular numbers)". OEIS Foundation. Retrieved 2016-05-21.
6. Sloane, N. J. A., ed. "Sequence A069099 (Centered heptagonal numbers)". OEIS Foundation. Retrieved 2016-05-21.
7. Sloane, N. J. A., ed. "Sequence A109611 (Chen primes)". OEIS Foundation. Retrieved 2016-05-21.
8. Guy, Richard; Unsolved Problems in Number Theory, p. 7 ISBN:1475717385
9. Sloane, N. J. A., ed. "Sequence A006753 (Smith numbers)". OEIS Foundation. Retrieved 2016-05-21.
10. Sloane, N. J. A., ed. "Sequence A076980 (Leyland numbers)". OEIS Foundation. Retrieved 2016-05-22.
11. Sloane, N. J. A., ed. "Sequence A001850 (Central Delannoy numbers)". OEIS Foundation. Retrieved 2016-05-21.
12. Sloane, N. J. A., ed. "Sequence A007304 (Sphenic numbers)". OEIS Foundation. Retrieved 2016-05-21.
13. Sloane, N. J. A., ed. "Sequence A000032 (Lucas numbers)". OEIS Foundation. Retrieved 2016-05-21.
14. Sloane, N. J. A., ed. "Sequence A001006 (Motzkin numbers)". OEIS Foundation. Retrieved 2016-05-22.
15. Sloane, N. J. A., ed. "Sequence A000384 (Hexagonal numbers)". OEIS Foundation. Retrieved 2016-05-22.
16. Sloane, N. J. A., ed. "Sequence A001106 (9-gonal numbers)". OEIS Foundation. Retrieved 2016-05-22.
17. Sloane, N. J. A., ed. "Sequence A060544 (Centered 9-gonal numbers)". OEIS Foundation. Retrieved 2016-05-22.
18. Sloane, N. J. A., ed. "Sequence A005278 (Noncototients)". OEIS Foundation. Retrieved 2016-05-21.
19. Sloane, N. J. A., ed. "Sequence A082897 (Perfect totient numbers)". OEIS Foundation. Retrieved 2016-05-22.
20. Sloane, N. J. A., ed. "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". OEIS Foundation. Retrieved 2022-06-02.
21. Sloane, N. J. A., ed. "Sequence A033950 (Refactorable numbers)". OEIS Foundation. Retrieved 2016-05-22.
22. Sloane, N. J. A., ed. "Sequence A100827 (Highly cototient numbers)". OEIS Foundation. Retrieved 2016-05-22.
23. Sloane, N. J. A., ed. "Sequence A000326 (Pentagonal numbers)". OEIS Foundation. Retrieved 2016-05-22.
24. Sloane, N. J. A., ed. "Sequence A036913 (Sparsely totient numbers)". OEIS Foundation. Retrieved 2016-05-22.
25. Sloane, N. J. A., ed. "Sequence A002407 (Cuban primes)". OEIS Foundation. Retrieved 2016-05-22.
26. Sloane, N. J. A., ed. "Sequence A005891 (Centered pentagonal numbers)". OEIS Foundation. Retrieved 2016-05-22.
27. Sloane, N. J. A., ed. "Sequence A003215 (Hex numbers)". OEIS Foundation. Retrieved 2016-05-22.
28. Sloane, N. J. A., ed. "Sequence A028442 (Numbers n such that Mertens' function is zero)". OEIS Foundation. Retrieved 2016-05-22.
29. Sloane, N. J. A., ed. "Sequence A003052 (Self numbers)". OEIS Foundation. Retrieved 2016-05-21.
30.
31. Sloane, N. J. A., ed. "Sequence A002858 (Ulam numbers)". OEIS Foundation.
32. Sloane, N. J. A., ed. "Sequence A000567 (Octagonal numbers)". OEIS Foundation. Retrieved 2016-05-22.
33. Sloane, N. J. A., ed. "Sequence A005898 (Centered cube numbers)". OEIS Foundation. Retrieved 2016-05-22.
34. Sloane, N. J. A., ed. "Sequence A005900 (Octahedral numbers)". OEIS Foundation. Retrieved 2016-05-22.
35. Sloane, N. J. A., ed. "Sequence A005385 (Safe primes)". OEIS Foundation. Retrieved 2016-05-22.
36. Sloane, N. J. A., ed. "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)". OEIS Foundation.
37. Sloane, N. J. A., ed. "Sequence A006036 (Primitive pseudoperfect numbers)". OEIS Foundation. Retrieved 2016-05-21.
38. Sloane, N. J. A., ed. "Sequence A000931 (Padovan sequence)". OEIS Foundation. Retrieved 2016-05-22.
39. Sloane, N. J. A., ed. "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". OEIS Foundation. Retrieved 2022-05-24.
40.
41. Sloane, N. J. A., ed. "Sequence A031971 (a(n) = Sum_{k=1..n} k^n)". OEIS Foundation.
42.
43. Sloane, N. J. A., ed. "Sequence A062786 (Centered 10-gonal numbers)". OEIS Foundation. Retrieved 2016-05-22.
44. Sloane, N. J. A., ed. "Sequence A005282 (Mian-Chowla sequence)". OEIS Foundation. Retrieved 2016-05-22.
45. Sloane, N. J. A., ed. "Sequence A000292 (Tetrahedral numbers)". OEIS Foundation. Retrieved 2016-05-22.
46. Sloane, N. J. A., ed. "Sequence A126796 (Number of complete partitions of n)". OEIS Foundation.
47. Sloane, N. J. A., ed. "Sequence A001608 (Perrin sequence)". OEIS Foundation. Retrieved 2016-05-22.
48. Sloane, N. J. A., ed. "Sequence A006562 (Balanced primes)". OEIS Foundation. Retrieved 2016-05-22.
49. Sloane, N. J. A., ed. "Sequence A000068 (Numbers k such that k^4 + 1 is prime)". OEIS Foundation.
50. Sloane, N. J. A., ed. "Sequence A003226 (Automorphic numbers)". OEIS Foundation. Retrieved 2016-05-22.
51. https://www.mathsisfun.com/puzzles/algebra-cow-solution.html
52. Sloane, N. J. A., ed. "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". OEIS Foundation. Retrieved 2022-06-02.
53. Sloane, N. J. A., ed. "Sequence A050918 (Woodall primes)". OEIS Foundation. Retrieved 2016-05-22.
54. Sloane, N. J. A., ed. "Sequence A072385 (Primes which can be represented as the sum of a prime and its reverse)". OEIS Foundation. Retrieved 2019-06-02.
55. Sloane, N. J. A., ed. "Sequence A000330 (Square pyramidal numbers)". OEIS Foundation. Retrieved 2016-05-22.
56. Sloane, N. J. A., ed. "Sequence A005897 (a(n) = 6*n^2 + 2 for n > 0, a(0)=1)". OEIS Foundation.
57. Sloane, N. J. A., ed. "Sequence A000569 (Number of graphical partitions of 2n)". OEIS Foundation.
58.
59. Sloane, N. J. A., ed. "Sequence A162862 (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)". OEIS Foundation. Retrieved 2022-06-02.
60. Sloane, N. J. A., ed. "Sequence A006318 (Large Schröder numbers)". OEIS Foundation. Retrieved 2016-05-22.