300 (number)

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

Mathematical properties
The number 300 is the 24th triangular number, with factorization 2$2$ × 3 × 5$2$.

It is the sum of a pair of twin primes, as well as a sum of ten consecutive primes:

$$ \begin{align} 300 & = 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47. \\ 300 & = 149 + 151. \\ \end{align}$$

Also, 30064 + 1 is prime.

300 is palindromic in three consecutive bases: 30010 = 6067 = 4548 = 3639, and also in base 13.

300 is the eighth term in the Engel expansion of pi, following 19 and preceding 1991.

309
309 = 3 &times; 103, Blum integer, number of primes <= 211.

312
312 = 23 &times; 3 &times; 13, idoneal number.

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

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

316
316 = 22 &times; 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.

319
319 = 11 &times; 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

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

321
321 = 3 &times; 107, a Delannoy number

322
322 = 2 &times; 7 &times; 23. 322 is a sphenic, nontotient, untouchable, and a Lucas number.

323
323 = 17 &times; 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 &times; 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 &times; 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 &times; 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 &times; 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 &times; 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 &times; 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number.

330
330 = 2 &times; 3 &times; 5 &times; 11. 330 is sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67), pentatope number (and hence a binomial coefficient $$\tbinom {11}4 $$), 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 &times; 83, Mertens function returns 0.

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

334
334 = 2 &times; 167, nontotient.

335
335 = 5 &times; 67. 335 is divisible by the number of primes below it, number of Lyndon words of length 12.

336
336 = 24 &times; 3 &times; 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 &times; 132, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.

339
339 = 3 &times; 113, Ulam number

340
340 = 22 &times; 5 &times; 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 and.

341
341 = 11 &times; 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 "bm&minus;1 &minus; 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.

342
342 = 2 &times; 32 &times; 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 &times; 43, octahedral number, noncototient, totient sum of the first 33 integers, refactorable number.

345
345 = 3 &times; 5 &times; 23, sphenic number, idoneal number

346
346 = 2 &times; 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 &times; 3 &times; 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.

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

350
350 = 2 &times; 52 &times; 7 = $\left\{ {7 \atop 4} \right\}$, 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 &times; 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 &times; 11, the number of n-Queens Problem solutions for n = 9. It is the sum of two consecutive primes (173 + 179), lazy caterer number

354
354 = 2 &times; 3 &times; 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 &times; 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 &times; 89, Mertens function returns 0.

357
357 = 3 &times; 7 &times; 17, sphenic number.

358
358 = 2 &times; 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.

361
361 = 192. 361 is a 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 &times; 181 = σ2(19): sum of squares of divisors of 19, Mertens function returns 0, nontotient, noncototient.

364
364 = 22 &times; 7 &times; 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.

366
366 = 2 &times; 3 &times; 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 &times; 23. It is also a Leyland number.

370
370 = 2 &times; 5 &times; 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 &times; 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 &times; 3 &times; 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), 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 &times; 11 &times; 17, sphenic number, nontotient, 3744 + 1 is prime.

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

376
376 = 23 &times; 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 &times; 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 &times; 33 &times; 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 first 15 odd primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53). 379! - 1 is prime.

380
380 = 22 &times; 5 &times; 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 &times; 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 &times; 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.

385
385 = 5 &times; 7 &times; 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 &times; 193, nontotient, noncototient, centered heptagonal number, number of surface points on a cube with edge-length 9.

387
387 = 32 &times; 43, number of graphical partitions of 22.

388
388 = 22 &times; 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.

390
390 = 2 &times; 3 &times; 5 &times; 13, sum of four consecutive primes (89 + 97 + 101 + 103), nontotient,
 * $$\sum_{n=0}^{10}{390}^{n}$$ is prime

391
391 = 17 &times; 23, Smith number, centered pentagonal number.

392
392 = 23 &times; 72, Achilles number.

393
393 = 3 &times; 131, Blum integer, Mertens function returns 0.

394
394 = 2 &times; 197 = S5 a Schröder number, nontotient, noncototient.

395
395 = 5 &times; 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 &times; 32 &times; 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 &times; 199, nontotient.
 * $$\sum_{n=0}^{10}{398}^{n}$$ is prime

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