300 __NOTOC__ Year 300 ( CCC) was a leap year starting on Monday of the Julian calendar. At the time, it was known as the Year of the Consulship of Constantius and Valerius (or, less frequently, year 1053 ''Ab urbe condita''). The denomination 300 ...

(three hundred) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following

299 __NOTOC__ Year 299 ( CCXCIX) was a common year starting on Sunday of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Diocletian and Maximian (or, less frequently, year 1052 ''Ab urbe condita''). The de ...

and preceding 301.

In Mathematics

300 is a composite number and the 24th

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

. It is also a second hexagonal number.

Integers from 301 to 399

300s

301

302

303

304

305

306

307

308

309

310s

310

311

312

313

314

315

315 = 3² × 5 × 7 =

D_ \!

, rencontres number, highly composite odd number, having 12 divisors. It is a

Harshad number In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers ...

, as it is divisible by the sum of its digits. It is a Zuckerman number, as it is divisible by the product of its digits.

316

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

centered heptagonal number A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by ...

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 number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...

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 In mathematics, a Delannoy number D counts the paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (''m'', ''n''), using only single steps north, northeast, or east. The Delannoy numbers are named after French army ...

322

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

Lucas number The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence ar ...

. It is also the first unprimeable number to end in 2.

323

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

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 In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...

\tbinom 4

), a

pentagonal number A pentagonal number is a figurate number that extends the concept of triangular number, triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotational ...

, 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 In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered polygonal number, centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot ...

, and Mertens function returns 0.

332

332 = 2² × 83, Mertens function returns 0.

333

333 = 3² × 37, Mertens function returns 0;

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ...

; 2³³³ is the smallest

power of two A power of two is a number of the form where is an integer, that is, the result of exponentiation with number 2, two as the Base (exponentiation), base and integer as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^ ...

greater than a

googol A googol is the large number 10100 or ten to the power of one hundred. In decimal notation, it is written as the digit 1 followed by one hundred zeros: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, ...

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, largely composite number.

337

337,

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

, emirp,

permutable prime A permutable prime, also known as anagrammatic prime, is a prime number which, in a given radix, base, can have its digits' positions switched through any permutation and still be a prime number. H. E. Richert, who is supposedly the first to stu ...

with 373 and 733, Chen prime,

star number In mathematics, a star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n' ...

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 o
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

342

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

343

343 = 7³, the first nice

Friedman number A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, ...

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 In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahedral ...

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

350s

350

350 = 2 × 5² × 7 =

\left\

, 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, 26th

, 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 * The international calling code for

Luxembourg Luxembourg, officially the Grand Duchy of Luxembourg, is a landlocked country in Western Europe. It is bordered by Belgium to the west and north, Germany to the east, and France on the south. Its capital and most populous city, Luxembour ...

353

* The international calling code for

Republic of Ireland Ireland ( ), also known as the Republic of Ireland (), is a country in Northwestern Europe, north-western Europe consisting of 26 of the 32 Counties of Ireland, counties of the island of Ireland, with a population of about 5.4 million. ...

354

354 = 2 × 3 × 59 = 1⁴ + 2⁴ + 3⁴ + 4⁴, sphenic number, nontotient, also

SMTP The Simple Mail Transfer Protocol (SMTP) is an Internet standard communication protocol for electronic mail transmission. Mail servers and other message transfer agents use SMTP to send and receive mail messages. User-level email clients typi ...

code meaning start of mail input. It is also sum of

absolute value In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if x is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), ...

of the

coefficient In mathematics, a coefficient is a Factor (arithmetic), multiplicative factor involved in some Summand, term of a polynomial, a series (mathematics), series, or any other type of expression (mathematics), expression. It may be a Dimensionless qu ...

s of Conway's polynomial. * The international calling code for

Iceland Iceland is a Nordic countries, Nordic island country between the Atlantic Ocean, North Atlantic and Arctic Oceans, on the Mid-Atlantic Ridge between North America and Europe. It is culturally and politically linked with Europe and is the regi ...

355

355 = 5 × 71, Smith number, Mertens function returns 0, divisible by the number of primes below it. The cototient of 355 is 75, 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.

357

357 = 3 × 7 × 17,

sphenic number In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definition A sphenic ...

358

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

359

360s

360

361

361 = 19². 361 is a centered triangular number,

centered octagonal number A centered octagonal number is a centered number, centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are th ...

, 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 A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular ...

, sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,

nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotie ...

. It is a

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

365

366

366 = 2 × 3 × 61,

, 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 A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) compared to a common year. The 366th day (or 13th month) is added to keep t ...

367

367 is a prime number, a lucky prime,

Perrin number In mathematics, the Perrin numbers are a doubly infinite constant-recursive sequence, constant-recursive integer sequence with Characteristic equation (calculus), characteristic equation . The Perrin numbers, named after the French engineer , bear ...

, 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 The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of t ...

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 In number theory, a noncototient is a positive integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it. That is, , where stands for Euler's totient function In number theory ...

, untouchable number, --> refactorable number.

373

373, prime number,

balanced prime In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, the nth prime number p_n is a balanced ...

, 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,

with 337 and 733, palindromic prime in 3 consecutive bases: 565₈ = 454₉ = 373₁₀ and also in base 4: 11311₄.

374

374 = 2 × 11 × 17,

, nontotient, 374⁴ + 1 is prime.

375

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

376

376 = 2³ × 47,

, 1- automorphic number, nontotient, refactorable number.

377

377 = 13 × 29,

Fibonacci number In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...

, a centered octahedral number, a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

378

378 = 2 × 3³ × 7, 27th

, 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.

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 A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

(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,

, square pyramidal number, the number of

integer partition In number theory and combinatorics, a partition of a non-negative integer , also called an integer partition, is a way of writing as a summation, sum of positive integers. Two sums that differ only in the order of their summands are considered ...

s 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 In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the ...

390s

390

390 = 2 × 3 × 5 × 13, sum of four consecutive primes (89 + 97 + 101 + 103), nontotient, :

\sum_^^

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 In mathematics, the Schröder number S_n, also called a ''large Schröder number'' or ''big Schröder number'', describes the number of lattice paths from the southwest corner (0,0) of an n \times n grid to the northeast corner (n,n), using only ...

, 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. :

\sum_^^

is prime

399

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

References

{{Integers, 3 Integers