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100,000,000

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From Wikipedia, the free encyclopedia
"Hundred million" redirects here. For the song by Treble Charger, see Hundred Million.

100000000
CardinalOne hundred million
Ordinal100000000th
(one hundred millionth)
Factorization28 × 58
Greek numeral
Roman numeralC
Binary1011111010111100001000000002
Ternary202220111120122013
Senary135312025446
Octal5753604008
Duodecimal295A645412
Hexadecimal5F5E10016

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 (simplified Chinese: 亿; traditional Chinese: 億; pinyin: yì) (or Chinese: 萬萬; pinyin: wànwàn in ancient texts), eok (억/億) and oku (億). 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)

[edit]

100,000,001 to 199,999,999

[edit]
  • 100,000,007 = smallest nine digit prime[1]
  • 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[2]
  • 105,413,504 = 147
  • 107,890,609 = Wedderburn-Etherington number[3]
  • 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[4]
  • 120,528,657 = number of centered hydrocarbons with 27 carbon atoms[5]
  • 121,242,121 = 110112, palindromic square
  • 122,522,400 = least number such that , where = sum of divisors of m[6]
  • 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[7]
  • 126,491,971 = Leonardo prime[8]
  • 129,140,163 = 317
  • 129,145,076 = Leyland number[9] using 3 & 17 (317 + 173)
  • 129,644,790 = Catalan number[10]
  • 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[11]
  • 130,691,232 = 425
  • 134,217,728 = 5123 = 89 = 227
  • 134,218,457 = Leyland number using 2 & 27 (227 + 272)
  • 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[12]
  • 136,048,896 = 116642 = 1084
  • 136,279,841 = The largest known Mersenne prime exponent, as of October 2024
  • 139,854,276 = 118262, the smallest zeroless base 10 pandigital square
  • 142,547,559 = Motzkin number[13]
  • 147,008,443 = 435
  • 148,035,889 = 121672 = 5293 = 236
  • 157,115,917 – number of parallelogram polyominoes with 24 cells.[14]
  • 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[15]
  • 177,264,449 = Leyland number using 8 & 9 (89 + 98)
  • 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 {1,2,...,11} and then partition each cell (block) into subcells.[16]
  • 190,899,322 = Bell number[17]
  • 191,102,976 = 138242 = 5763 = 246
  • 192,622,052 = number of free 18-ominoes
  • 193,707,721 = smallest prime factor of 267 − 1, a number that Mersenne claimed to be prime
  • 199,960,004 = number of surface-points of a tetrahedron with edge-length 9999[18]

200,000,000 to 299,999,999

[edit]
  • 200,000,002 = number of surface-points of a tetrahedron with edge-length 10000[18]
  • 205,962,976 = 465
  • 210,295,326 = Fine number
  • 211,016,256 = number of primitive polynomials of degree 33 over GF(2)[19]
  • 212,890,625 = 1-automorphic number[20]
  • 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[21]
  • 225,331,713 = self-descriptive number in base 9
  • 229,345,007 = 475
  • 232,792,560 = superior highly composite number;[22] colossally abundant number;[23] smallest number divisible by the numbers from 1 to 22 (there is no smaller number divisible by the numbers from 1 to 20 since any number divisible by 3 and 7 must be divisible by 21 and any number divisible by 2 and 11 must be divisible by 22)
  • 240,882,152 = number of signed trees with 16 nodes[24]
  • 244,140,625 = 156252 = 1253 = 256 = 512
  • 244,389,457 = Leyland number[9] using 5 & 12 (512 + 125)
  • 244,330,711 = n such that n | (3n + 5)[25]
  • 245,492,244 = number of 35-bead necklaces (turning over is allowed) where complements are equivalent[7]
  • 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[11]
  • 253,450,711 = Wedderburn-Etherington prime[3]
  • 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[12]
  • 267,914,296 = Fibonacci number
  • 268,435,456 = 163842 = 1284 = 167 = 414 = 228
  • 268,436,240 = Leyland number using 2 & 28 (228 + 282)
  • 268,473,872 = Leyland number using 4 & 14 (414 + 144)
  • 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[2]
  • 282,475,249 = 168072 = 495 = 710
  • 292,475,249 = Leyland number using 7 & 10 (710 + 107)
  • 294,130,458 = number of prime knots with 19 crossings

300,000,000 to 399,999,999

[edit]
  • 308,915,776 = 175762 = 6763 = 266
  • 309,576,725 = number of centered hydrocarbons with 28 carbon atoms[5]
  • 312,500,000 = 505
  • 321,534,781 = Markov prime
  • 331,160,281 = Leonardo prime[8]
  • 333,333,333 = repdigit
  • 336,849,900 = number of primitive polynomials of degree 34 over GF(2)[19]
  • 345,025,251 = 515
  • 350,238,175 = number of reduced trees with 37 nodes[15]
  • 362,802,072 – number of parallelogram polyominoes with 25 cells[14]
  • 364,568,617 = Leyland number[9] using 6 & 11 (611 + 116)
  • 365,496,202 = n such that n | (3n + 5)[25]
  • 367,567,200 = 14th colossally abundant number,[23] 14th superior highly composite number[22]
  • 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 using 3 & 18 (318 + 183)

400,000,000 to 499,999,999

[edit]
  • 400,080,004 = 200022, palindromic square
  • 400,763,223 = Motzkin number[13]
  • 404,090,404 = 201022, palindromic square
  • 404,204,977 = number of prime numbers having ten digits[26]
  • 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[27]
  • 444,101,658 = number of (unordered, unlabeled) rooted trimmed trees with 27 nodes[28]
  • 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[29]
  • 477,353,376 = number of 36-bead necklaces (turning over is allowed) where complements are equivalent[7]
  • 477,638,700 = Catalan number[10]
  • 479,001,599 = factorial prime[30]
  • 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[11]
  • 499,999,751 = Sophie Germain prime

500,000,000 to 599,999,999

[edit]
  • 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[12]
  • 522,808,225 = 228652, palindromic square
  • 535,828,591 = Leonardo prime[8]
  • 536,870,911 = third composite Mersenne number with a prime exponent
  • 536,870,912 = 229
  • 536,871,753 = Leyland number[9] using 2 & 29 (229 + 292)
  • 542,474,231 = k such that the sum of the squares of the first k primes is divisible by k.[31]
  • 543,339,720 = Pell number[21]
  • 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 [32]
  • 575,023,344 = 14-th derivative of xx at x=1[33]
  • 594,823,321 = 243892 = 8413 = 296
  • 596,572,387 = Wedderburn-Etherington prime[3]

600,000,000 to 699,999,999

[edit]
  • 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 (594 + 1584 = 1334 + 1344), 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

[edit]
  • 701,408,733 = Fibonacci number
  • 714,924,299 = 595
  • 715,497,037 = number of reduced trees with 38 nodes[15]
  • 715,827,883 = Wagstaff prime,[34] Jacobsthal prime
  • 725,594,112 = number of primitive polynomials of degree 36 over GF(2)[19]
  • 729,000,000 = 270002 = 9003 = 306
  • 742,624,232 = number of free 19-ominoes
  • 751,065,460 = number of trees with 27 unlabeled nodes[2]
  • 774,840,978 = Leyland number[9] using 9 & 9 (99 + 99)
  • 777,600,000 = 605
  • 777,777,777 = repdigit
  • 778,483,932 = Fine number
  • 780,291,637 = Markov prime
  • 787,109,376 = 1-automorphic number[20]
  • 797,790,928 = number of centered hydrocarbons with 29 carbon atoms[5]

800,000,000 to 899,999,999

[edit]
  • 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.[14]
  • 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[35]
  • 893,871,739 = 197
  • 895,745,041 = 1734

900,000,000 to 999,999,999

[edit]
  • 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[7]
  • 929,275,200 = number of primitive polynomials of degree 35 over GF(2)[19]
  • 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[12]
  • 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

References

[edit]
  1. ^ Sloane, N. J. A. (ed.). "Sequence A003617 (Smallest n-digit prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ a b c Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000022 (Number of centered hydrocarbons with n atoms)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A134716 (least number m such that sigma(m)/m > n, where sigma(m) is the sum of divisors of m)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ a b c Sloane, N. J. A. (ed.). "Sequence A145912 (Prime Leonardo numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A076980 (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)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ a b Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000013 (Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000031 (Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ a b Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^ a b c Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  15. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A000110 (Bell or exponential numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ a b Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A011260 (Number of primitive polynomials of degree n over GF(2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ a b Sloane, N. J. A. (ed.). "Sequence A003226 (Automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ a b Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^ a b Sloane, N. J. A. (ed.). "Sequence A002201 (Superior highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ^ a b Sloane, N. J. A. (ed.). "Sequence A004490 (Colossally abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A000060 (Number of signed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^ a b Sloane, N. J. A. (ed.). "Sequence A277288 (Positive integers n such that n divides (3^n + 5))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  27. ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  28. ^ Sloane, N. J. A. (ed.). "Sequence A002955 (Number of (unordered, unlabeled) rooted trimmed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  29. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  30. ^ Sloane, N. J. A. (ed.). "Sequence A088054 (Factorial primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  31. ^ Sloane, N. J. A. (ed.). "Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A031971 (Sum_{1..n} k^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. ^ Sloane, N. J. A. (ed.). "Sequence A005727 (n-th derivative of x^x at x equals 1. Also called Lehmer-Comtet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  34. ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ^ Sloane, N. J. A. (ed.). "Sequence A030984 (2-automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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