100,000,000 Explained

Number:	100000000
Cardinal:	One hundred million
Factorization:	2^8 × 5^8
Roman:	C

100,000,000 (one hundred million) is the natural number following 99,999,999 and preceding 100,000,001.

In scientific notation, it is written as 10⁸.

East Asian languages treat 100,000,000 as a counting unit, significant as the square of a myriad, also a counting unit. In Chinese, Korean, and Japanese respectively it is yi (or in ancient texts), eok (Korean: 억/億) and oku . These languages do not have single words for a thousand to the second, third, fifth powers, etc.

100,000,000 is also the fourth power of 100 and also the square of 10000.

Selected 9-digit numbers (100,000,001–999,999,999)

100,000,001 to 199,999,999

• 100,000,007 = smallest nine digit prime
• 100,005,153 = smallest triangular number with 9 digits and the 14,142nd triangular number
• 100,020,001 = 10001², palindromic square
• 100,544,625 = 465³, the smallest 9-digit cube
• 102,030,201 = 10101², palindromic square
• 102,334,155 = Fibonacci number
• 102,400,000 = 40⁵
• 104,060,401 = 10201² = 101⁴, palindromic square
• 104,636,890 = number of trees with 25 unlabeled nodes
• 105,413,504 = 14⁷
• 107,890,609 = Wedderburn-Etherington number
• 111,111,111 = repunit, square root of 12345678987654321
• 111,111,113 = Chen prime, Sophie Germain prime, cousin prime.
• 113,379,904 = 10648² = 484³ = 22⁶
• 115,856,201 = 41⁵
• 119,481,296 = logarithmic number
• 120,528,657 = number of centered hydrocarbons with 27 carbon atoms
• 121,242,121 = 11011², palindromic square
• 122,522,400 = least number

m such that (\sigma(m))/(m) > 5 , where \sigma(m) = sum of divisors of m

• 123,454,321 = 11111², palindromic square
• 123,456,789 = smallest zeroless base 10 pandigital number
• 125,686,521 = 11211², palindromic square
• 126,390,032 = number of 34-bead necklaces (turning over is allowed) where complements are equivalent
• 126,491,971 = Leonardo prime
• 129,140,163 = 3¹⁷
• 129,145,076 = Leyland number^[1]
• 129,644,790 = Catalan number
• 130,150,588 = number of 33-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 130,691,232 = 42⁵
• 134,217,728 = 512³ = 8⁹ = 2²⁷
• 134,218,457 = Leyland number^[1]
• 134,219,796 = number of 32-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple 32-stage cycling shift register; also number of binary irreducible polynomials whose degree divides 32
• 136,048,896 = 11664² = 108⁴
• 139,854,276 = 11826², the smallest zeroless base 10 pandigital square
• 142,547,559 = Motzkin number
• 147,008,443 = 43⁵
• 148,035,889 = 12167² = 529³ = 23⁶
• 157,115,917 – number of parallelogram polyominoes with 24 cells.
• 157,351,936 = 12544² = 112⁴
• 164,916,224 = 44⁵
• 165,580,141 = Fibonacci number
• 167,444,795 = cyclic number in base 6
• 170,859,375 = 15⁷
• 171,794,492 = number of reduced trees with 36 nodes
• 177,264,449 = Leyland number^[1]
• 179,424,673 = 10,000,000th prime number
• 184,528,125 = 45⁵
• 185,794,560 = double factorial of 18
• 188,378,402 = number of ways to partition and then partition each cell (block) into subcells.
• 190,899,322 = Bell number
• 191,102,976 = 13824² = 576³ = 24⁶
• 192,622,052 = number of free 18-ominoes
• 199,960,004 = number of surface-points of a tetrahedron with edge-length 9999

200,000,000 to 299,999,999

• 200,000,002 = number of surface-points of a tetrahedron with edge-length 10000
• 205,962,976 = 46⁵
• 210,295,326 = Fine number
• 211,016,256 = number of primitive polynomials of degree 33 over GF(2)
• 212,890,625 = 1-automorphic number
• 214,358,881 = 14641² = 121⁴ = 11⁸
• 222,222,222 = repdigit
• 222,222,227 = safe prime
• 223,092,870 = the product of the first nine prime numbers, thus the ninth primorial
• 225,058,681 = Pell number
• 225,331,713 = self-descriptive number in base 9
• 229,345,007 = 47⁵
• 232,792,560 = superior highly composite number; colossally abundant number; smallest number divisible by the numbers from 1 to 22
• 240,882,152 = number of signed trees with 16 nodes
• 244,140,625 = 15625² = 125³ = 25⁶ = 5¹²
• 244,389,457 = Leyland number^[1]
• 244,330,711 = n such that n | (3ⁿ + 5)
• 245,492,244 = number of 35-bead necklaces (turning over is allowed) where complements are equivalent
• 252,648,992 = number of 34-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 253,450,711 = Wedderburn-Etherington prime
• 254,803,968 = 48⁵
• 260,301,176 = number of 33-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple 33-stage cycling shift register; also number of binary irreducible polynomials whose degree divides 33
• 267,914,296 = Fibonacci number
• 268,435,456 = 16384² = 128⁴ = 16⁷ = 4¹⁴ = 2²⁸
• 268,436,240 = Leyland number^[1]
• 268,473,872 = Leyland number^[1]
• 272,400,600 = the number of terms of the harmonic series required to pass 20
• 275,305,224 = the number of magic squares of order 5, excluding rotations and reflections
• 279,793,450 = number of trees with 26 unlabeled nodes
• 282,475,249 = 16807² = 49⁵ = 7¹⁰
• 292,475,249 = Leyland number^[1]
• 294,130,458 = number of prime knots with 19 crossings

300,000,000 to 399,999,999

• 308,915,776 = 17576² = 676³ = 26⁶
• 309,576,725 = number of centered hydrocarbons with 28 carbon atoms
• 312,500,000 = 50⁵
• 321,534,781 = Markov prime
• 331,160,281 = Leonardo prime
• 333,333,333 = repdigit
• 336,849,900 = number of primitive polynomials of degree 34 over GF(2)
• 345,025,251 = 51⁵
• 350,238,175 = number of reduced trees with 37 nodes
• 362,802,072 – number of parallelogram polyominoes with 25 cells
• 364,568,617 = Leyland number^[1]
• 365,496,202 = n such that n | (3ⁿ + 5)
• 367,567,200 = colossally abundant number, superior highly composite number
• 380,204,032 = 52⁵
• 381,654,729 = the only polydivisible number that is also a zeroless pandigital number
• 387,420,489 = 19683² = 729³ = 27⁶ = 9⁹ = 3¹⁸ and in tetration notation ²9
• 387,426,321 = Leyland number^[1]

400,000,000 to 499,999,999

• 400,080,004 = 20002², palindromic square
• 400,763,223 = Motzkin number
• 404,090,404 = 20102², palindromic square
• 404,204,977 = number of prime numbers having ten digits
• 405,071,317 = 1¹ + 2² + 3³ + 4⁴ + 5⁵ + 6⁶ + 7⁷ + 8⁸ + 9⁹
• 410,338,673 = 17⁷
• 418,195,493 = 53⁵
• 429,981,696 = 20736² = 144⁴ = 12⁸ = 100,000,000₁₂ AKA a gross-great-great-gross (100₁₂ great-great-grosses)
• 433,494,437 = Fibonacci prime, Markov prime
• 442,386,619 = alternating factorial
• 444,101,658 = number of (unordered, unlabeled) rooted trimmed trees with 27 nodes
• 444,444,444 = repdigit
• 455,052,511 = number of primes under 10¹⁰
• 459,165,024 = 54⁵
• 467,871,369 = number of triangle-free graphs on 14 vertices
• 477,353,376 = number of 36-bead necklaces (turning over is allowed) where complements are equivalent
• 477,638,700 = Catalan number
• 479,001,599 = factorial prime
• 479,001,600 = 12!
• 481,890,304 = 21952² = 784³ = 28⁶
• 490,853,416 = number of 35-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 499,999,751 = Sophie Germain prime

500,000,000 to 599,999,999

• 503,284,375 = 55⁵
• 505,294,128 = number of 34-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple 34-stage cycling shift register; also number of binary irreducible polynomials whose degree divides 34
• 522,808,225 = 22865², palindromic square
• 535,828,591 = Leonardo prime
• 536,870,911 = third composite Mersenne number with a prime exponent
• 536,870,912 = 2²⁹
• 536,871,753 = Leyland number^[1]
• 542,474,231 = k such that the sum of the squares of the first k primes is divisible by k.
• 543,339,720 = Pell number
• 550,731,776 = 56⁵
• 554,999,445 = a Kaprekar constant for digit length 9 in base 10
• 555,555,555 = repdigit
• 574,304,985 = 1⁹ + 2⁹ + 3⁹ + 4⁹ + 5⁹ + 6⁹ + 7⁹ + 8⁹ + 9⁹
• 575,023,344 = 14-th derivative of x^x at x=1
• 594,823,321 = 24389² = 841³ = 29⁶
• 596,572,387 = Wedderburn-Etherington prime

600,000,000 to 699,999,999

• 601,692,057 = 57⁵
• 612,220,032 = 18⁷
• 617,323,716 = 24846², palindromic square
• 635,318,657 = the smallest number that is the sum of two fourth powers in two different ways, of which Euler was aware.
• 644,972,544 = 864³, 3-smooth number
• 654,729,075 = double factorial of 19
• 656,356,768 = 58⁵
• 666,666,666 = repdigit
• 670,617,279 = highest stopping time integer under 10⁹ for the Collatz conjecture

700,000,000 to 799,999,999

• 701,408,733 = Fibonacci number
• 714,924,299 = 59⁵
• 715,497,037 = number of reduced trees with 38 nodes
• 715,827,883 = Wagstaff prime, Jacobsthal prime
• 725,594,112 = number of primitive polynomials of degree 36 over GF(2)
• 729,000,000 = 27000² = 900³ = 30⁶
• 742,624,232 = number of free 19-ominoes
• 751,065,460 = number of trees with 27 unlabeled nodes
• 774,840,978 = Leyland number^[1]
• 777,600,000 = 60⁵
• 777,777,777 = repdigit
• 778,483,932 = Fine number
• 780,291,637 = Markov prime
• 787,109,376 = 1-automorphic number
• 797,790,928 = number of centered hydrocarbons with 29 carbon atoms

800,000,000 to 899,999,999

• 810,810,000 = smallest number with exactly 1000 factors
• 815,730,721 = 13⁸
• 815,730,721 = 169⁴
• 835,210,000 = 170⁴
• 837,759,792 – number of parallelogram polyominoes with 26 cells.
• 844,596,301 = 61⁵
• 855,036,081 = 171⁴
• 875,213,056 = 172⁴
• 887,503,681 = 31⁶
• 888,888,888 – repdigit
• 893,554,688 = 2-automorphic number
• 893,871,739 = 19⁷
• 895,745,041 = 173⁴

900,000,000 to 999,999,999

• 906,150,257 = smallest counterexample to the Polya conjecture
• 916,132,832 = 62⁵
• 923,187,456 = 30384², the largest zeroless pandigital square
• 928,772,650 = number of 37-bead necklaces (turning over is allowed) where complements are equivalent
• 929,275,200 = number of primitive polynomials of degree 35 over GF(2)
• 942,060,249 = 30693², palindromic square
• 981,706,832 = number of 35-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple 35-stage cycling shift register; also number of binary irreducible polynomials whose degree divides 35
• 987,654,321 = largest zeroless pandigital number
• 992,436,543 = 63⁵
• 997,002,999 = 999³, the largest 9-digit cube
• 999,950,884 = 31622², the largest 9-digit square
• 999,961,560 = largest triangular number with 9 digits and the 44,720th triangular number
• 999,999,937 = largest 9-digit prime number
• 999,999,999 = repdigit

Notes and References

1. Leyland numbers: 3, together with numbers expressible as n^k + k^n nontrivially, i.e., n,k > 1 (to avoid n = (n-1)^1 + 1^(n-1)).