300 (number)

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

In mathematics

300 is a composite number and the 24th triangular number. It is also a second hexagonal number.

Integers from 301 to 399

300s

301

301 = 7 × 43. It is a Stirling number of the second kind represented by {7/3} because there are 301 ways to organize 7 objects into 3 non-empty sets. It is a happy number, meaning that infinitely taking the sum of the squares of its digits will eventually result in 1. 301 is a lazy caterer number because it is the maximum number of pieces that can be made by cutting a circle with 24 cuts. It is the sum of three consecutive primes: 301 = 97 + 101 + 103.

302

302 = 2 × 151. 302 is a happy number because repeatedly taking the sum of the squares of the digits of 302 will eventually result in 1. It is a nontotient number because it is an even number and phi(x)=302 has no solutions. There are 302 prime partitions of 40 meaning that there are 302 ways to separate 40 into the sum of prime parts.

303

303 = 3 × 101. 303 is a semiprime number becauuse it has only 2 prime factors. It is a palindromic number. There are 303 compositions of 10 where they cannot be viewed as a stack. There are 303 bipartite graphs with 8 vertices.

304

304 = 24 × 19. It is a primitive semiperfect number because it is a semiperfect number that is not divisible by any other semiperfect number. It is an untouchable number because it is not equal to the sum of any number's proper divisors. 304 is a nontotient number because it is an even number and phi(x) = 304 has no solution. It is the sum of consecutive primes in two different ways:

304 = 41+43+47+53+59+61 = 23+29+31+37+41+43+47+53.

305

305 = 5 × 61. It is the fifth hexagonal prism number which is defined by (n+1)(3n2+3n+1). It is the convolution of the first 7 primes with themselves. It is the hypotenuse of two Pythagorean triples: 3052=2072+2242=1362+2732.

306

306 = 2 × 32 × 17. It is the 17th oblong number meaning that it is equal to 17*18. It is an untouchable number meaning that it cannot be equal to the sum of proper factors in any number. It is the sum of four consecutive primes (71+73+79+83).

There are 306 triangular numbers with 5 digits.

307

307 is an isolated (i.e., not twin) prime, but because 309 is a semiprime, 307 is a Chen prime. 307 is the third non-palindromic number to have a palindromic square. 3072=94249.

307 is one of only 16 natural numbers for which the imaginary quadratic field Q ( − n ) {\displaystyle \mathbb {Q} ({\sqrt {-n}})} has class number 3.

There are 307 one-sided noniamonds meaning that it is the number of ways to organize 9 triangles with each one touching at least one other on the edge.

There are 307 solid partitions of 7.

308

308 = 22 × 7 × 11. It is a nontotient, a heptagonal pyramidal number, and the sum of two consecutive primes (151 + 157). It is the totient sum of the first 41 integers.

309

309 = 3 × 103. It is a Blum integer and a centered icosahedral number.

310s

310

310 = 2 × 5 × 31. It is a sphenic number meaning that it has 3 prime factors. It is a noncototient number because m − φ(m) = 310 has no solutions. There are 310 Dyks 11 paths with strictly intersecting peaks. The sum of the divisors of 310 is a perfect square.

311

311 is a twin prime with 313, an irregular prime, an emirp, and a permutable prime with 113 and 131. It is an Eisenstein prime with no imaginary part and real part of the form 3 n − 1 {\displaystyle 3n-1} and a Gaussian prime with no imaginary part and real part of the form 4 n − 1 {\displaystyle 4n-1}.

It can be expressed as a sum of consecutive primes in four different ways: as a sum of three consecutive primes (101 + 103 + 107), as a sum of five consecutive primes (53 + 59 + 61 + 67 + 71), as a sum of seven consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59), and as a sum of eleven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

311 is a strictly non-palindromic number, as it is not palindromic in any base between base 2 and base 309.

311 is the smallest positive integer d such that the imaginary quadratic field Q(√–d) has a class number of 19.

4311 - 3311 is a prime number.

For all integers n from 1 to 42, the value of 311 * log2(n) is within ¼ of an integer.

312

312 = 23 × 3 × 13. It is a Idoneal number and a practical number. It is a semiperfect number, as it is equal to the sum of some or all of its divisors. It is a Harshad number, as it is divisible by the sum of its digits. It is part of a Pythagorean triple.

313

313 is a twin prime with 311, a Pythagorean prime, a regular prime, a truncatable prime, a weakly prime in base 5, and a palindromic prime in both decimal and binary. It is also the smallest number which is a full full reptend prime in base 10 but not in base 2 to 9. It is an index of a prime Lucas number, a centered square number, and a happy number.

314

314 = 2 × 157.It is a nontotient and a squarefree semiprime. It forms a Pythagorean triple with 170 and 264. It is also what the first three digits of π (pi) would look like if the decimal point was removed.

315

315 = 32 × 5 × 7. It is a rencontres number and a highly composite odd number.

316

316 = 22 × 79. It is a centered triangular number, a centered heptagonal number, an Ulam number, and a member of one Tetranacci sequence. It appears in counting asymmetric polyominoes and binary-matrix involutions.

317

317 is a Chen prime and an Eisenstein prime with no imaginary part. It is one of the rare primes that is both right and left truncatable, that is, one can remove the rightmost or leftmost digit, resulting in 31 and 17 respectively, both of which are still prime. It is one of only two 3-digit primes satisfying the equation as p:

2 p + p = q

where p and q are both prime.

317 is also a strictly non-palindromic number.

317 is the telephone area code for the city of Indianapolis, Indiana, United States and its surrounding counties. Because of this, the city celebrates 317 Day on March 17 (3/17), which has become a major cultural event in the city.

318

318 is a sphenic number, a nontotient and the sum of 12 consecutive primes, 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47. There are 318 posets with 6 unlabeled elements.

319

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

320s

320

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

321

321 = 3 × 107. It is a Delannoy number

322

322 = 2 × 7 × 23. It is a sphenic, a nontotient, an untouchable number, and a Lucas number. It is also the first unprimeable number to end in 2.

323

323 is a semiprime, and the product of two consecutive prime numbers (17 × 19). It is also the sum of nine consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53) and the sum of the 13 consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47)

323 is the eighth Motzkin number, M 8 {\displaystyle M_{8}}, meaning there are 323 ways to draw non-intersecting chords between eight points on a circle.

323 is the first Lucas pseudoprime with parameters (P, Q) defined by Selfridge's method. Additionally, it is the first Fibonacci pseudoprime (Lucas pseudoprime with P = 1 and Q = -1).

324

325

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

326

326 = 2 × 163. It is a nontotient, a noncototient, an untouchable number, and a lazy caterer number. It is the sum of the 14 consecutive primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

327

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

328

328 = 23 × 41. It is a refactorable number. 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. It is a highly cototient number. It is the sum of three consecutive primes (107 + 109 + 113).

330s

330

330 = 2 × 3 × 5 × 11. It is a pentatope number (a binomial coefficient ( 11 4 ) {\displaystyle {\tbinom {11}{4}}}), a pentagonal number, and a sparsely totient number. It is sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67).

331

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

332

332 = 22 × 83. It is a zero of Mertens function.

333

333 = 32 × 37. It is a zero of Mertens function and a repdigit.

2333 is the smallest power of two greater than a googol.

334

334 = 2 × 167. It is a nontotient.

335

335 = 5 × 67. There are 335 Lyndon words of length 12.

336

336 = 24 × 3 × 7. It is an untouchable number and a largely composite number. There are 336 partitions of 41 into prime parts.

337

337 is a prime number, an emirp, a permutable prime, and a Chen prime.

338

338 = 2 × 132. It is a nontotient. There are 338 square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.

339

339 = 3 × 113. It is an Ulam number.

340s

340

340 = 22 × 5 × 17. It is a noncototient and a nontotient.

It is the sum of the first four powers of 4 (41 + 42 + 43 + 44), the sum of eight consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), and the sum of ten consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).

There are 340 regions formed by drawing the line segments connecting any two of the 12 perimeter points of a 3 times 3 grid of squares (sequenceA331452in theOEIS) and (sequenceA255011in theOEIS). [clarification needed]

341

341 is an octagonal number, a centered cube number, and a super-Poulet number. It is a palindrome and repdigit in bases 2 (1010101012), 4 (111114), 8 (5258), 17 (13117) and 30 (BB30). It is the sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61).

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. It is a pronic number, and an 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. It is an octahedral number, a noncototient, a refactorable number, and the totient sum of the first 33 integers.

345

345 = 3 × 5 × 23. It is a sphenic number and an idoneal number.

346

346 = 2 × 173. It is a Smith number and a noncototient.

347

347 is a prime number, an emirp, a safe prime, an Eisenstein prime with no imaginary part, a Chen prime, a twin prime with 349, a strictly non-palindromic number, and a Friedman prime since 347 = 73 + 4.

348

348 = 22 × 3 × 29. It is a refactorable number. It is the sum of four consecutive primes (79 + 83 + 89 + 97).

349

349 is a prime number, a twin prime with 347, and a lucky prime. It is the sum of three consecutive primes (109 + 113 + 127).

5349 - 4349 is a prime number.

350s

350

350 = 2 × 52 × 7. It is a primitive semiperfect number and a nontotient. A truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

350= { 7 4 } {\displaystyle \left\{{7 \atop 4}\right\}}, making 350 a stirling number of the second kind.

351

351 = 33 × 13. It is a member of the Padovan sequence and the 26th triangular number. It is the sum of five consecutive primes (61 + 67 + 71 + 73 + 79). There are 351 compositions of 15 into distinct parts.

352

352 = 25 × 11. It is a lazy caterer number and the sum of two consecutive primes (173 + 179). There are 352 n-Queens Problem solutions for n = 9.

353

354

354 = 2 × 3 × 59 = 14 + 24 + 34 + 44. It is a sphenic number and a nontotient. It is also sum of absolute value of the coefficients of Conway's polynomial.

355

355 = 5 × 71. It is a Smith number and a zero of Mertens function. The cototient of 355 is 75, where 75 is the product of its digits (3 x 5 x 5 = 75).

It is the numerator of, 355/113, the best simplified rational approximation of pi having a denominator of four digits or fewer, known as Milü.

356

356 = 22 × 89. It is a zero of Mertens function.

357

357 = 3 × 7 × 17. It is a sphenic number.

358

358 = 2 × 179. It is a zero of Mertens function and the sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71). There are 358 ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.[bettersourceneeded]

359

359 is an Eisenstein prime with no imaginary part and a Chen prime. It is a strictly non-palindromic number.

360s

360

361

361 = 192. 361 is a centered triangular number, a centered octagonal number, a centered decagonal number and a member of the Mian–Chowla sequence. There are 361 intersections on a standard 19 x 19 Go board.

362

362 = 2 × 181. It is a zero of Mertens function, a nontotient, a noncototient.

362= σ2(19), the sum of squares of divisors of 19.

363

363=3 × 112. It is a deficient number, a perfect totient number, a zero of Mertens function, and a repdigit (BB) in base 32. It is a palindromic number in bases 3, 10, 11 and 32. It is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59) and the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).

363 can be expressed as the sum of three squares in four different ways:

363 = 112 + 112 + 112 = 52 + 72 + 172 = 12 + 12 + 192 = 132 + 132 + 52.

363 cubits is the solution given to Rhind Mathematical Papyrus question 50 – find the side length of an octagon with the same area as a circle 9 khet in diameter.

364

364 = 22 × 7 × 13. It is a tetrahedral number, a zero of Mertens function, a nontotient, and the sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).

It is a repdigit in base 3 (111111), base 9 (444), base 25 (EE), base 27 (DD), base 51 (77) and base 90 (44).

365

366

366 = 2 × 3 × 61. It is a sphenic number, a zero of Mertens function, a noncototient, a 26-gonal number, and a 123-gonal number. There are 366 complete partitions of 20.

There are 366 days in a leap year.

367

367 is a prime number, a lucky prime, a Perrin number, a happy number in base 10, a prime index prime and a strictly non-palindromic number.

368

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

369

369 = 32 × 41. 369 is the magic constant of the 9×9 magic square and the n-Queens Problem for n=9. 369 forms a Ruth-Aaron Pair with 370 because the sums of their prime factors are equal.

There are 369 free octominoes (polyominoes of order 8).

370s

370

370 = 2 × 5 × 37. It is a sphenic number, a nontotient, and a Base 10 Armstrong number since 33 + 73 + 03 = 370. It forms a Ruth–Aaron pair with only distinct prime factors counted with 369. It is the sum of four consecutive primes (83 + 89 + 97 + 101).

371

371 = 7 × 53. It is an Armstrong number since 33 + 73 + 13 = 371. It is the sum of the primes from its least to its greatest prime factor, the next such composite number is 2935561623745. It is the sum of three consecutive primes (113 + 127 + 131) and the sum of seven consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67).

372

372 = 22 × 3 × 31. It is a noncototient, an untouchable number, and a refactorable number. It is the sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).

373

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

374

374 = 2 × 11 × 17. It is a sphenic number and a nontotient. 3744 + 1 is prime.

375

375 = 3 × 53. There are 375 regions in regular 11-gon with all diagonals drawn.

376

376 = 23 × 47. It is a pentagonal number, a 1-automorphic number, a nontotient, and a refactorable number.

377

377 is a semiprime and a deficient number. 377 is the 7th centered octahedral number and the 14th nonzero member of the Fibonacci sequence.

378

378 = 2 × 33 × 7. It is a cake number, a hexagonal number, and a Smith number. It is the 27th triangular number.

379

379 is a prime number, a Chen prime, a 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.

380s

380

380 = 22 × 5 × 19. It is a pronic number. There are 380 regions when a figure made up of a row of 6 adjacent congruent rectangles is divided by drawing the diagonals of all possible rectangles.

381

381 = 3 × 127. It is 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. It is a Smith number. It is the sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).

383

383 is a prime number, a safe prime, a Woodall prime, a Thabit number, an Eisenstein prime with no imaginary part, and a 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. It is a sphenic number and a square pyramidal number. There are 385 integer partitions of 18.

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

386

386 = 2 × 193. It is a nontotient, a noncototient, and a centered heptagonal number. There are 388 surface points on a cube with edge-length 9.

387

387 = 32 × 43. There are 387 graphical partitions of 22.

388

388 = 22 × 97. It is the solution to the postage stamp problem with 6 stamps and 6 denominations. There are 388 uniform rooted trees with 10 nodes.

389

389 is a prime number, an emirp, an Eisenstein prime with no imaginary part, a Chen prime, a highly cototient number, a strictly non-palindromic number. It is the smallest conductor of a rank 2 Elliptic curve.

390s

390

390 = 2 × 3 × 5 × 13. It is a nontotient and the sum of four consecutive primes (89 + 97 + 101 + 103).

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

391

391 = 17 × 23. It is a Smith number and a centered pentagonal number.

392

392 = 23 × 72. It is an Achilles number.

393

393 = 3 × 131. It is a Blum integer and a zero of Mertens function.

394

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

395

395 = 5 × 79. There are 395 (unordered, unlabeled) rooted trimmed trees with 11 nodes.

395 is sum of three consecutive primes (127 + 131 + 137) and the sum of five consecutive primes (71 + 73 + 79 + 83 + 89).

396

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

397

397 is a prime number, a cuban prime, and a centered hexagonal number.

398

398 = 2 × 199. It is a nontotient.

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

399

399 = 3 × 7 × 19=4 5 − 5 4 {\displaystyle 4^{5}-5^{4}}. It is a sphenic number, a Leyland number of the second kind,and the smallest Lucas–Carmichael number.

399! + 1 is prime.

399 is the largest number whose base 10 digit sum is larger than the square root of the number: 3 + 9 + 9 = 21, which is larger than 19.975.