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100,000

From Wikipedia, the free encyclopedia
(Redirected from 10**5)
"100000" redirects here. For other uses, see 100000 (disambiguation).
← 99999 100000 100001 →
Cardinalone hundred thousand
Ordinal100000th
(one hundred thousandth)
Factorization25 × 55
Greek numeral
Roman numeralC
Binary110000110101000002
Ternary120020112013
Senary20505446
Octal3032408
Duodecimal49A5412
Hexadecimal186A016
Egyptian hieroglyph𓆐

100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.

Terms for 100,000

[edit]

In Bangladesh, India, Pakistan and South Asia, one hundred thousand is called a lakh, and is written as 1,00,000. The Thai, Lao, Khmer and Vietnamese languages also have separate words for this number: แสน, ແສນ, សែន (all saen), and ức respectively. The Malagasy word is hetsy.[1]

In the Netherlands, a 'ton' is a colloquialism for a denomination of 100.000 monetary units. In the guilders period a ton would denote 100.000 guilders. With the introduction of the euro, a ton would come to mean 100.000 euros. The usage is mostly limited to the financial sphere and the buying and selling of houses. It is not used in official settings because of the ambiguity with commonly used metric tonne. While usage is common in the Netherlands, it sees almost no use in Belgium.[citation needed]

In Cyrillic numerals, it is known as the legion (легион): or .

Values of 100,000

[edit]

In astronomy, 100,000 metres, 100 kilometres, or 100 km (62 miles) is the altitude at which the Fédération Aéronautique Internationale (FAI) defines spaceflight to begin.

In paleoclimatology, the 100,000-year problem is a mismatch between the temperature record and the modeled incoming solar radiation.

In the Irish language, céad míle fáilte (pronounced [ˌceːd̪ˠ ˈmʲiːlʲə ˈfˠaːl̠ʲtʲə]) is a popular greeting meaning "a hundred thousand welcomes".

Selected 6-digit numbers (100,001–999,999)

[edit]

100,001 to 199,999

[edit]
  • 147,640 = Keith number[15]
  • 148,149 = Kaprekar number[25]
  • 152,381 = unique prime in base 20
  • 156,146 = Keith number[15]
  • 155,921 = smallest prime number being the only prime in an interval from 100n to 100n + 99
  • 160,000 = 204
  • 160,176 = number of reduced trees with 26 nodes[26]
  • 161,051 = 115
  • 161,280 = highly totient number[5]
  • 166,320 = highly composite number[11]
  • 167,400 = harmonic divisor number[8]
  • 167,894 = number of ways to partition {1,2,3,4,5,6,7,8} and then partition each cell (block) into subcells.[27]
  • 173,525 = number of partitions of 49[7]
  • 173,600 = harmonic divisor number[8]
  • 174,680 = Keith number[15]
  • 174,763 = Wagstaff prime[28]
  • 176,906 = number of 24-bead necklaces (turning over is allowed) where complements are equivalent[29]
  • 177,147 = 311
  • 177,777 = smallest natural number requiring 19 syllables in American English, 21 in British English
  • 178,478 = Leyland number[23]
  • 181,440 = highly totient number[5]
  • 181,819 = Kaprekar number[25]
  • 182,362 = number of 23-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[30]
  • 183,186 = Keith number[15]
  • 183,231 = number of partially ordered set with 9 unlabeled elements[31]
  • 187,110 = Kaprekar number[25]
  • 189,819 = number of letters in the longest English word, taking 3 hours to pronounce[32]
  • 194,481 = 214
  • 195,025 = Pell number,[33] Markov number[24]
  • 196,418 = Fibonacci number,[16] Markov number[24]
  • 196,560 = the kissing number in 24 dimensions
  • 196,883 = the dimension of the smallest nontrivial irreducible representation of the Monster group
  • 196,884 = the coefficient of q in the Fourier series expansion of the j-invariant. The adjacency of 196883 and 196884 was important in suggesting monstrous moonshine.
  • 199,999 = prime number.

200,000 to 299,999

[edit]
  • 202,717 = k such that the sum of the squares of the first k primes is divisible by k.[34]
  • 206,098 – Large Schröder number
  • 206,265 = rounded number of arc seconds in a radian (see also parsec), since ⁠180 × 60 × 60/π⁠ = 206,264.806...
  • 207,360 = highly totient number[5]
  • 208,012 = the Catalan number C12[35]
  • 208,335 = the largest number to be both triangular and square pyramidal[36]
  • 208,495 = Kaprekar number[25]
  • 212,159 = smallest unprimeable number ending in 1, 3, 7 or 9[37][38]
  • 221,760 = highly composite number[11]
  • 222,222 = repdigit
  • 224,737 = the 20,000th prime number
  • 227,475 = Riordan number
  • 234,256 = 224
  • 237,510 = harmonic divisor number[8]
  • 238,591 = number of free 13-ominoes
  • 241,920 = highly totient number[5]
  • 242,060 = harmonic divisor number[8]
  • 248,832 = 125, 100,00012, AKA a gross-great-gross (10012 great-grosses); the smallest fifth power that can be represented as the sum of only 6 fifth powers: 125 = 45 + 55 + 65 + 75 + 95 + 115
  • 253,293 = number of prime knots with 15 crossings
  • 255,168 = number of ways to play tic tac toe[39]
  • 262,144 = 218; exponential factorial of 4;[40] a superperfect number[41]
  • 262,468 = Leyland number[23]
  • 268,705 = Leyland number[23]
  • 271,129 – smallest known Sierpiński prime
  • 274,177 = prime factor of the Fermat number F6
  • 275,807/195,025 ≈ √2
  • 276,480 = number of primitive polynomials of degree 24 over GF(2)[14]
  • 277,200 = highly composite number[11]
  • 279,841 = 234
  • 279,936 = 67
  • 280,859 = a prime number whose square 78881777881 is tridigital
  • 291,400 = number of non-equivalent ways of expressing 100,000,000 as the sum of two prime numbers[42]
  • 293,547 = Wedderburn–Etherington number[20]
  • 294,001 = smallest weakly prime number in base 10[43]
  • 294,685 = Markov number[24]
  • 298,320 = Keith number[15]

300,000 to 399,999

[edit]
  • 310,572 = Motzkin number[12]
  • 314,159 = pi-prime
  • 316,749 = number of reduced trees with 27 nodes[26]
  • 317,811 = Fibonacci number[16]
  • 317,955 = number of trees with 19 unlabeled nodes[18]
  • 318,682 = Kaprekar number[25]
  • 325,878 = Fine number[44]
  • 326,981 = alternating factorial[45]
  • 329,967 = Kaprekar number[25]
  • 331,776 = 244
  • 332,640 = highly composite number;[11] harmonic divisor number[8]
  • 333,333 = repdigit
  • 333,667 = sexy prime and unique prime[46]
  • 333,673 = sexy prime with 333,679
  • 333,679 = sexy prime with 333,673
  • 337,500 = 22 × 33 × 55
  • 337,594 = number of 25-bead necklaces (turning over is allowed) where complements are equivalent[29]
  • 349,716 = number of 24-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[30]
  • 351,351 = only known odd abundant number that is not the sum of some of its proper, nontrivial (i.e. >1) divisors (sequence A122036 in the OEIS).
  • 351,352 = Kaprekar number[25]
  • 355,419 = Keith number[15]
  • 356,643 = Kaprekar number[25]
  • 356,960 = number of primitive polynomials of degree 23 over GF(2)[14]
  • 360,360 = harmonic divisor number;[8] smallest number divisible by the numbers from 1 to 15 (there is no smaller number divisible by the numbers from 1 to 14 since any number divisible by 3 and 5 must be divisible by 15)
  • 362,880 = 9!, highly totient number[5]
  • 369,119 = prime number which divides the sum of all primes less than or equal to it[47]
  • 369,293 = smallest prime with the property that inserting a digit anywhere in the number will always yield a composite[48]
  • 370,261 = first prime followed by a prime gap of over 100
  • 371,293 = 135, palindromic in base 12 (15AA5112)
  • 389,305 = self-descriptive number in base 7
  • 390,313 = Kaprekar number[25]
  • 390,625 = 58
  • 397,585 = Leyland number[23]

400,000 to 499,999

[edit]
  • 409,113 = sum of the first nine factorials
  • 422,481 = smallest number whose fourth power is the sum of three smaller fourth powers
  • 423,393 = Leyland number[23]
  • 426,389 = Markov number[24]
  • 426,569 = cyclic number in base 12
  • 437,760 to 440,319 = any of these numbers will cause the Apple II+ and Apple IIe computers to crash to a monitor prompt when entered at the BASIC prompt, due to a short-cut in the Applesoft code programming of the overflow test when evaluating 16-bit numbers.[49] Entering 440000 at the prompt has been used to hack games that are protected against entering commands at the prompt after the game is loaded.
  • 444,444 = repdigit
  • 456,976 = 264
  • 461,539 = Kaprekar number[25]
  • 466,830 = Kaprekar number[25]
  • 470,832 = Pell number[33]
  • 483,840 = highly totient number[5]
  • 492,638 = number of signed trees with 12 nodes[9]
  • 498,960 = highly composite number[11]
  • 499,393 = Markov number[24]
  • 499,500 = Kaprekar number[25]

500,000 to 599,999

[edit]
  • 500,500 = Kaprekar number,[25] sum of first 1,000 integers
  • 509,203 = Riesel prime[50]
  • 510,510 = the product of the first seven prime numbers, thus the seventh primorial.[51] It is also the product of four consecutive Fibonacci numbers—13, 21, 34, 55, the largest such sequence of any length to be also a primorial. And it is a double triangular number, the sum of all even numbers from 0 to 1428.
  • 514,229 = Fibonacci prime,[52]
  • 518,859 = Schröder–Hipparchus number[4]
  • 524,287 = Mersenne prime[21]
  • 524,288 = 219
  • 524,649 = Leyland number[23]
  • 525,600 = minutes in a non-leap year
  • 527,040 = minutes in a leap year
  • 531,441 = 312
  • 533,169 = Leyland number[23]
  • 533,170 = Kaprekar number[25]
  • 537,824 = 145
  • 539,400 = harmonic divisor number[8]
  • 548,834 = equal to the sum of the sixth powers of its digits
  • 554,400 = highly composite number[11]
  • 555,555 = repdigit
  • 586,081 = number of prime numbers having seven digits.[53]
  • 599,999 = prime number.

600,000 to 699,999

[edit]
  • 604,800 = number of seconds in a week
  • 614,656 = 284
  • 625,992 = Riordan number
  • 629,933 = number of reduced trees with 28 nodes[26]
  • 645,120 = double factorial of 14
  • 646,018 = Markov number[24]
  • 649,532 = number of 26-bead necklaces (turning over is allowed) where complements are equivalent[29]
  • 664,579 = the number of primes under 10,000,000
  • 665,280 = highly composite number[11]
  • 665,857/470,832 ≈ √2
  • 666,666 = repdigit
  • 671,092 = number of 25-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[30]
  • 676,157 = Wedderburn–Etherington number[20]
  • 678,570 = Bell number[13]
  • 694,280 = Keith number[15]
  • 695,520 = harmonic divisor number[8]

700,000 to 799,999

[edit]
  • 700,001 = prime number.
  • 707,281 = 294
  • 720,720 = superior highly composite number;[54] colossally abundant number;[55] smallest number divisible by the numbers from 1 to 16
  • 725,760 = highly totient number[5]
  • 726,180 = harmonic divisor number[8]
  • 729,000 = 903
  • 739,397 = largest prime that is both right- and left-truncatable.
  • 742,900 = Catalan number[35]
  • 753,480 = harmonic divisor number[8]
  • 759,375 = 155
  • 762,701 – smallest known composite Riesel number
  • 765,623 = emirp, Friedman prime 56 × 72 − 6 ÷ 3
  • 777,777 = repdigit, smallest natural number requiring 20 syllables in American English, 22 in British English, largest number in English not containing the letter 'i' in its name
  • 783,700 = initial number of third century xx00 to xx99 (after 400 and 1,400) containing seventeen prime numbers[56][a] {783,701, 783,703, 783,707, 783,719, 783,721, 783,733, 783,737, 783,743, 783,749, 783,763, 783,767, 783,779, 783,781, 783,787, 783,791, 783,793, 783,799}
  • 799,999 = prime number.

800,000 to 899,999

[edit]
  • 810,000 = 304
  • 823,065 = number of trees with 20 unlabeled nodes[18]
  • 823,543 = 77
  • 825,265 = smallest Carmichael number with 5 prime factors
  • 832,040 = Fibonacci number[16]
  • 853,467 = Motzkin number[12]
  • 857,375 = 953
  • 873,612 = 11 + 22 + 33 + 44 + 55 + 66 + 77
  • 888,888 = repdigit
  • 890,625 = automorphic number[10]

900,000 to 999,999

[edit]
"999999" redirects here. For the string of nines in pi, see Six nines in pi.
  • 900,001 = prime number
  • 901,971 = number of free 14-ominoes
  • 909,091 = unique prime in base 10
  • 923,521 = 314
  • 925,765 = Markov number[24]
  • 925,993 = Keith number[15]
  • 950,976 = harmonic divisor number[8]
  • 956,619: 956619^2=915119911161, and only the digits 1, 5, 6 and 9 are used in both this number and its square.
  • 967,680 = highly totient number[5]
  • 970,299 = 993, the largest 6-digit cube
  • 998,001 = 9992, the largest 6-digit square. The reciprocal of this number, in its expanded form, lists all three-digit numbers in order except 998.[58]
  • 998,991 = largest triangular number with 6 digits and the 1413th triangular number
  • 999,983 = largest 6-digit prime number
  • 999,999 = repdigit. Rational numbers with denominators 7 and 13 have 6-digit repetends when expressed in decimal form, because 999999 is the smallest number one less than a power of 10 that is divisible by 7 and by 13, and it is the largest number in English not containing the letter 'l' in its name.

Prime numbers

[edit]

There are 9,592 primes less than 105, where 99,991 is the largest prime number smaller than 100,000.

Increments of 105 from 100,000 through a one million have the following prime counts:

  • 8,392 primes between 100,000 and 200,000.[b] This is a difference of 1,200 primes from the previous range.
    • 104,729 is the 10,000th prime, which is in this range.
    • 199,999 is prime.
  • 8,013 primes between 200,000 and 300,000.[c] A difference of 379 primes from the previous range.
    • 224,737 is the 20,000th prime.
  • 7,863 primes between 300,000 and 400,000.[d] A difference of 150 primes from the previous range.
    • 350,377 is the 30,000th prime.
  • 7,678 primes between 400,000 and 500,000.[e] A difference of 185 primes from the previous range. Here, the difference increases by a count of 35.
    • 479,909 is the 40,000th prime.
  • 7,560 primes between 500,000 and 600,000.[f] A difference of 118 primes from the previous range.
    • 7,560 is the twentieth highly composite number.[11]
    • 599,999 is prime.
  • 7,445 primes between 600,000 and 700,000.[g] A difference of 115 primes from the previous range.
    • 611,953 is the 50,000th prime.
  • 7,408 primes between 700,000 and 800,000.[h] A difference of 37 primes from the previous range.
    • 700,001 and 799,999 are both prime.
    • 746,773 is the 60,000th prime.
  • 7,323 primes between 800,000 and 900,000.[i] A difference of 85 primes from the previous range. Here, the difference increases by a count of 48.
    • 882,377 is the 70,000th prime.
  • 7,224 primes between 900,000 and 1,000,000.[j] A difference of 99 primes from the previous range. The difference increases again, by a count of 14.
    • 900,001 is prime.

In total, there are 68,906 prime numbers between 100,000 and 1,000,000.[59]

Notes

[edit]
  1. ^ There are no centuries containing more than seventeen primes between 200 and 122,853,771,370,899 inclusive.[57]
  2. ^ Smallest p > 100,000 is 100,003 (9,593rd); largest p < 200,000 is 199,999 (17,984th).
  3. ^ Smallest p > 200,000 is 200,003 (17,985th); largest p < 300,000 is 299,993 (25,997th).
  4. ^ Smallest p > 300,000 is 300,007 (25,998th); largest p < 400,000 is 399,989 (33,860th).
  5. ^ Smallest p > 400,000 is 400,009 (33,861st); largest p < 500,000 is 499,979 (41,538th).
  6. ^ Smallest p > 500,000 is 500,009 (41,539th); largest p < 600,000 is 599,999 (49,098th).
  7. ^ Smallest p > 600,000 is 600,011 (49,099th); largest p < 700,000 is 699,967 (56,543rd).
  8. ^ Smallest p > 700,000 is 700,001 (56,544th); largest p < 800,000 is 799,999 (63,951st).
  9. ^ Smallest p > 800,000 is 800,011 (63,952nd); largest p < 900,000 is 899,981 (71,274th).
  10. ^ Smallest p > 900,000 is 900,001 (71,275th); largest p < 1,000,000 is 999,983 (78,498th).

References

[edit]
  1. ^ "Malagasy Dictionary and Madagascar Encyclopedia : hetsy". malagasyword.org. 26 October 2017. Retrieved 2019-12-31.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A003617 (Smallest n-digit prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ "Problem of the Month (August 2000)". Archived from the original on 2012-12-18. Retrieved 2013-01-13.
  4. ^ a b Sloane, N. J. A. (ed.). "Sequence A001003 (Schroeder's second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ a b c d e f g h i j k l m Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ a b Sloane, N. J. A. (ed.). "Sequence A000060 (Number of signed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ a b Sloane, N. J. A. (ed.). "Sequence A003226 (Automorphic numbers: m^2 ends with m)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ a b c Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ a b Sloane, N. J. A. (ed.). "Sequence A000110 (Bell or exponential numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^ a b c 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.
  15. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A049363 (a(1) = 1; for n > 1, smallest digitally balanced number in base n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ 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.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ a b c Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ a b Sloane, N. J. A. (ed.). "Sequence A000668 (Mersenne primes (primes of the form 2^n - 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A003432 (Hadamard maximal determinant problem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-30.
  23. ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^ a b c d e f g h i j k l m n Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ^ 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.
  27. ^ 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.
  28. ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  29. ^ a b c 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.
  30. ^ 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.
  31. ^ Sloane, N. J. A. (ed.). "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^ "The longest word in English? Here are the top 15 biggest ones". Berlitz. Retrieved 2024-03-01.
  33. ^ a b Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  34. ^ 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.
  35. ^ a b Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  36. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  37. ^ Collins, Julia (2019). Numbers in Minutes. United Kingdom: Quercus. p. 140. ISBN 978-1635061772.
  38. ^ Sloane, N. J. A. (ed.). "Sequence A143641 (Odd prime-proof numbers not ending in 5)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  39. ^ "How many Tic-Tac-Toe (Noughts and crosses) games?".
  40. ^ Sloane, N. J. A. (ed.). "Sequence A049384 (a(0)=1, a(n+1) = (n+1)^a(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  41. ^ Sloane, N. J. A. (ed.). "Sequence A019279 (Superperfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  42. ^ Sloane, N. J. A. (ed.). "Sequence A065577 (Number of Goldbach partitions of 10^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  43. ^ Weißstein, Eric W. (25 December 2020). "Weakly Prime". Wolfram MathWorld.
  44. ^ Sloane, N. J. A. (ed.). "Sequence A000957 (Fine's sequence (or Fine numbers): number of relations of valence greater than or equal to 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  45. ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  46. ^ Sloane, N. J. A. (ed.). "Sequence A040017 (Unique period primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  47. ^ Sloane, N. J. A. (ed.). "Sequence A007506 (Primes p with property that p divides the sum of all primes <= p)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  48. ^ Sloane, N. J. A. (ed.). "Sequence A125001 (Non-insertable primes: primes with property that no matter where you insert (or prepend or append) a digit you get a composite number (except for prepending a zero).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  49. ^ "Applesoft Disassembly -- S.d912". Archived from the original on 2016-04-15. Retrieved 2016-04-04. Disassembled ROM. See comments at $DA1E.
  50. ^ Sloane, N. J. A. (ed.). "Sequence A101036 (Riesel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A002110 (Primorial numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  52. ^ Sloane, N. J. A. (ed.). "Sequence A005478 (Prime Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.Sloane, N. J. A. (ed.). "Sequence A178444 (Markov numbers that are prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  53. ^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  54. ^ Sloane, N. J. A. (ed.). "Sequence A002201 (Superior highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  55. ^ Sloane, N. J. A. (ed.). "Sequence A004490 (Colossally abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  56. ^ Sloane, N. J. A. (ed.). "Sequence A186509 (Centuries containing 17 primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  57. ^ Sloane, N. J. A. (ed.). "Sequence A186311 (Least century 100k to 100k+99 with exactly n primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  58. ^ "Dividing one by 998001 produces list of three digit numbers". 23 January 2012.
  59. ^ Caldwell, Chris K. "The Nth Prime Page". PrimePages. Retrieved 2022-12-03. From the differences of the prime indexes of the smallest and largest prime numbers in ranges of increments of 105, plus 1 (for each range).
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