100,000,000

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 \frac{\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 using 3 & 17 (317 + 173)
• 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 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
• 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
• 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 using 8 & 9 (89 + 98)
• 178,956,971 = smallest composite Wagstaff number with prime index
• 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.
• 190,899,322 = Bell number
• 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

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 (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
• 244,140,625 = 156252 = 1253 = 256 = 512
• 244,389,457 = Leyland number using 5 & 12 (512 + 125)
• 244,330,711 = n such that n | (3n + 5)
• 245,044,800 = first highly composite number that is not a Harshad number
• 245,492,244 = number of 35-bead necklaces (turning over is allowed) where complements are equivalent
• 252,047,376 = 158762 = 1264
• 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 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
• 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
• 299,792,458 = the exact definition of the speed of light in a vacuum, in metres per second

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 using 6 & 11 (611 + 116)
• 365,496,202 = n such that n | (3n + 5)
• 367,567,200 = 14th colossally abundant number, 14th 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 using 3 & 18 (318 + 183)

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 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.
• 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 xx 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
• 648,646,704 = , where φ is the Euler's totient function
• 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 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
• 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 = 1694, 138
• 835,210,000 = 1704
• 837,759,792 – number of parallelogram polyominoes with 26 cells.
• 839,296,300 – initial number of first century xx00 to xx99 containing at least sixteen prime numbers {839,296,301, 839,296,303, 839,296,309, 839,296,319, 839,296,321, 839,296,327, 839,296,331, 839,296,333, 839,296,349, 839,296,351, 839,296,357, 839,296,361, 839,296,373, 839,296,379, 839,296,397, 839,296,399} since 2,705,000
• 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 base-10 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 base-10 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

References

References

1. {{Cite OEIS. A003617. Smallest n-digit prime
2. {{cite OEIS. A000055. Number of trees with n unlabeled nodes
3. {{Cite OEIS. A001190. Wedderburn-Etherington numbers
4. {{cite OEIS. A002104. Logarithmic numbers
5. {{cite OEIS. A000022. Number of centered hydrocarbons with n atoms
6. {{cite OEIS. A134716. least number m such that sigma(m)/m > n, where sigma(m) is the sum of divisors of m
7. {{cite OEIS. A000011. Number of n-bead necklaces (turning over is allowed) where complements are equivalent
8. {{Cite OEIS. A145912. Prime Leonardo numbers
9. {{Cite OEIS. A076980
10. {{Cite OEIS. A000108. Catalan numbers
11. {{cite OEIS. 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
12. {{cite OEIS. 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
13. {{Cite OEIS. A001006. Motzkin numbers
14. {{cite OEIS. A006958. Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused)
15. {{cite OEIS. A000014. Number of series-reduced trees with n nodes
16. {{cite OEIS. A000258. Expansion of e.g.f. exp(exp(exp(x)-1)-1)
17. {{Cite OEIS. A000110. Bell or exponential numbers
18. {{cite OEIS. A005893. Number of points on surface of tetrahedron
19. {{cite OEIS. A011260. Number of primitive polynomials of degree n over GF(2)
20. {{Cite OEIS. A003226. Automorphic numbers
21. {{Cite OEIS. A000129. Pell numbers
22. {{Cite OEIS. A002201. Superior highly composite numbers
23. {{Cite OEIS. A004490. Colossally abundant numbers
24. {{cite OEIS. A000060. Number of signed trees with n nodes
25. {{cite OEIS. A277288. Positive integers n such that n divides (3^n + 5)
26. {{Cite OEIS. A006879. Number of primes with n digits
27. {{Cite OEIS. A005165. Alternating factorials
28. {{cite OEIS. A002955. Number of (unordered, unlabeled) rooted trimmed trees with n nodes
29. {{cite OEIS. A006785. Number of triangle-free graphs on n vertices
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32. {{cite OEIS. A031971. Sum_{1..n} k^n
33. {{cite OEIS. A005727. n-th derivative of x^x at x equals 1. Also called Lehmer-Comtet numbers
34. {{Cite OEIS. A000979. Wagstaff primes
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36. {{Cite OEIS. A186509. Centuries containing 17 primes
37. {{Cite OEIS. A030984. 2-automorphic numbers