100,000

From HandWiki
Short description: Natural number
← 99999 100000 100001 →
Cardinalone hundred thousand
Ordinal100000th
(one hundred thousandth)
Factorization25 × 55
Greek numeral[math]\displaystyle{ \stackrel{\iota}{\Mu} }[/math]
Roman numeralC
Binary110000110101000002
Ternary120020112013
Quaternary1201222004
Quinary112000005
Senary20505446
Octal3032408
Duodecimal49A5412
Hexadecimal186A016
VigesimalCA0020
Base 36255S36

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

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 Cyrillic numerals, it is known as the legion (легион): Legion-1000000-Cyrillic.svg or Несведь.svg.

Values of 100,000

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 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)

100,001 to 199,999

200,000 to 299,999

  • 202,717 = k such that the sum of the squares of the first k primes is divisible by k.[27]
  • 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[4]
  • 208,012 = the Catalan number C12[28]
  • 208,335 = the largest number to be both triangular and square pyramidal
  • 208,495 = Kaprekar number[19]
  • 212,159 = smallest unprimeable number ending in 1, 3, 7 or 9[29][30]
  • 221,760 = highly composite number[8]
  • 222,222 = repdigit
  • 227,475 = Riordan number
  • 234,256 = 224
  • 237,510 = harmonic divisor number[6]
  • 238,591 = number of free 13-ominoes
  • 241,920 = highly totient number[4]
  • 242,060 = harmonic divisor number[6]
  • 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
  • 262,144 = 218; exponential factorial of 4;[31] a superperfect number[32]
  • 262,468 = Leyland number[17]
  • 268,705 = Leyland number[17]
  • 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)[11]
  • 277,200 = highly composite number[8]
  • 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[33]
  • 293,547 = Wedderburn–Etherington number[15]
  • 294,001 = smallest weakly prime number in base 10[34]
  • 294,685 = Markov number[18]
  • 298,320 = Keith number[12]

300,000 to 399,999

  • 310,572 = Motzkin number[9]
  • 316,749 = number of reduced trees with 27 nodes[20]
  • 317,811 = Fibonacci number[13]
  • 318,682 = Kaprekar number[19]
  • 325,878 = Fine number[35]
  • 326,981 = alternating factorial[36]
  • 329,967 = Kaprekar number[19]
  • 331,776 = 244
  • 332,640 = highly composite number;[8] harmonic divisor number[6]
  • 333,333 = repdigit
  • 333,667 = sexy prime and unique prime[37]
  • 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[23]
  • 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[24]
  • 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[19]
  • 355,419 = Keith number[12]
  • 356,643 = Kaprekar number[19]
  • 356,960 = number of primitive polynomials of degree 23 over GF(2)[11]
  • 360,360 = harmonic divisor number;[6] the smallest number divisible by all of the numbers 1 through 15
  • 362,880 = 9!, highly totient number[4]
  • 369,119 = prime number which divides the sum of all primes less than or equal to it[38]
  • 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[19]
  • 390,625 = 58
  • 397,585 = Leyland number[17]

400,000 to 499,999

  • 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[17]
  • 426,389 = Markov number[18]
  • 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.[39] 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[19]
  • 466,830 = Kaprekar number[19]
  • 470,832 = Pell number[26]
  • 483,840 = highly totient number[4]
  • 498,960 = highly composite number[8]
  • 499,393 = Markov number[18]
  • 499,500 = Kaprekar number[19]

500,000 to 599,999

  • 500,500 = Kaprekar number,[19] sum of first 1,000 integers
  • 509,203 = Riesel number[40]
  • 510,510 = the product of the first seven prime numbers, thus the seventh primorial.[41] It is also the product of four consecutive Fibonacci numbers—13, 21, 34, 55, the highest 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,[42] Markov prime[18]
  • 518,859 = little Schroeder number
  • 524,287 = Mersenne prime[16]
  • 524,288 = 219
  • 524,649 = Leyland number[17]
  • 525,600 = minutes in a non-leap year
  • 527,040 = minutes in a leap year
  • 531,441 = 312
  • 533,169 = Leyland number[17]
  • 533,170 = Kaprekar number[19]
  • 537,824 = 145
  • 539,400 = harmonic divisor number[6]
  • 548,834 = equal to the sum of the sixth powers of its digits
  • 554,400 = highly composite number[8]
  • 555,555 = repdigit
  • 586,081 = number of prime numbers having seven digits.[43]
  • 599,999 = prime number.

600,000 to 699,999

  • 604,800 = number of seconds in a week
  • 614,656 = 284
  • 625,992 = Riordan number
  • 629,933 = number of reduced trees with 28 nodes[20]
  • 646,018 = Markov number[18]
  • 649,532 = number of 26-bead necklaces (turning over is allowed) where complements are equivalent[23]
  • 664,579 = the number of primes under 10,000,000
  • 665,280 = highly composite number[8]
  • 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[24]
  • 676,157 = Wedderburn–Etherington number[15]
  • 678,570 = Bell number[10]
  • 694,280 = Keith number[12]
  • 695,520 = harmonic divisor number[6]

700,000 to 799,999

  • 700,001 = prime number.
  • 707,281 = 294
  • 720,720 = superior highly composite number;[44] colossally abundant number;[45] the smallest number divisible by all the numbers 1 through 16
  • 725,760 = highly totient number[4]
  • 726,180 = harmonic divisor number[6]
  • 729,000 = 903
  • 739,397 = largest prime that is both right- and left-truncatable.
  • 742,900 = Catalan number[28]
  • 753,480 = harmonic divisor number[6]
  • 759,375 = 155
  • 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[46][lower-alpha 1] {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

  • 810,000 = 304
  • 823,543 = 77
  • 825,265 = smallest Carmichael number with 5 prime factors
  • 832,040 = Fibonacci number[13]
  • 853,467 = Motzkin number[9]
  • 857,375 = 953
  • 873,612 = 11 + 22 + 33 + 44 + 55 + 66 + 77
  • 888,888 = repdigit
  • 890,625 = 1-automorphic number[7]

900,000 to 999,999

  • 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[18]
  • 925,993 = Keith number[12]
  • 950,976 = harmonic divisor number[6]
  • 967,680 = highly totient number[4]
  • 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.[48]
  • 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

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:

This is a difference of 1,200 primes from the previous range.
104,729 is the 10,000th prime in this range.
199,999 is prime.
A difference of 379 primes from the previous range.
224,737 is the 20,000th prime.
A difference of 150 primes from the previous range.
350,377 is the 30,000th prime.
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.
A difference of 118 primes from the previous range.
7,560 is the twentieth highly composite number.[49]
599,999 is prime.
A difference of 115 primes from the previous range.
611,953 is the 50,000th prime.
A difference of 37 primes from the previous range.
700,001 and 799,999 are both prime.
746,773 is the 60,000th prime.
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.
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.[50]

Notes

  1. ↑ There are no centuries containing more than seventeen primes between 200 and 122,853,771,370,899 inclusive.[47]
  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

  1. ↑ "Malagasy Dictionary and Madagascar Encyclopedia : hetsy". 26 October 2017. http://malagasyword.org/bins/teny2/hetsy. 
  2. ↑ Sloane, N. J. A., ed. "Sequence A003617 (Smallest n-digit prime)". OEIS Foundation. https://oeis.org/A003617. Retrieved 7 September 2017. 
  3. ↑ "Problem of the Month (August 2000)". http://www2.stetson.edu/~efriedma/mathmagic/0800.html. 
  4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Sloane, N. J. A., ed. "Sequence A097942 (Highly totient numbers)". OEIS Foundation. https://oeis.org/A097942. Retrieved 2016-06-17. 
  5. ↑ Sloane, N. J. A., ed. "Sequence A006785 (Number of triangle-free graphs on n vertices)". OEIS Foundation. https://oeis.org/A006785. 
  6. ↑ 6.00 6.01 6.02 6.03 6.04 6.05 6.06 6.07 6.08 6.09 6.10 6.11 6.12 Sloane, N. J. A., ed. "Sequence A001599 (Harmonic or Ore numbers)". OEIS Foundation. https://oeis.org/A001599. Retrieved 2016-06-17. 
  7. ↑ 7.0 7.1 Sloane, N. J. A., ed. "Sequence A003226 (Automorphic numbers)". OEIS Foundation. https://oeis.org/A003226. Retrieved 2019-04-06. 
  8. ↑ 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 Sloane, N. J. A., ed. "Sequence A002182 (Highly composite numbers)". OEIS Foundation. https://oeis.org/A002182. Retrieved 2016-06-17. 
  9. ↑ 9.0 9.1 9.2 Sloane, N. J. A., ed. "Sequence A001006 (Motzkin numbers)". OEIS Foundation. https://oeis.org/A001006. Retrieved 2016-06-17. 
  10. ↑ 10.0 10.1 Sloane, N. J. A., ed. "Sequence A000110 (Bell or exponential numbers)". OEIS Foundation. https://oeis.org/A000110. Retrieved 2016-06-17. 
  11. ↑ 11.0 11.1 11.2 Sloane, N. J. A., ed. "Sequence A011260 (Number of primitive polynomials of degree n over GF(2))". OEIS Foundation. https://oeis.org/A011260. 
  12. ↑ 12.0 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 Sloane, N. J. A., ed. "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)access-date=2016-06-17)". OEIS Foundation. https://oeis.org/A007629. 
  13. ↑ 13.0 13.1 13.2 13.3 Sloane, N. J. A., ed. "Sequence A000045 (Fibonacci numbers)". OEIS Foundation. https://oeis.org/A000045. Retrieved 2016-06-17. 
  14. ↑ Sloane, N. J. A., ed. "Sequence A002104 (Logarithmic numbers)". OEIS Foundation. https://oeis.org/A002104. 
  15. ↑ 15.0 15.1 15.2 Sloane, N. J. A., ed. "Sequence A001190 (Wedderburn-Etherington numbers)". OEIS Foundation. https://oeis.org/A001190. Retrieved 2016-06-17. 
  16. ↑ 16.0 16.1 Sloane, N. J. A., ed. "Sequence A000668 (Mersenne primes)". OEIS Foundation. https://oeis.org/A000668. Retrieved 2016-06-17. 
  17. ↑ 17.0 17.1 17.2 17.3 17.4 17.5 17.6 17.7 Sloane, N. J. A., ed. "Sequence A076980 (Leyland numbers)". OEIS Foundation. https://oeis.org/A076980. Retrieved 2016-06-17. 
  18. ↑ 18.0 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 Sloane, N. J. A., ed. "Sequence A002559 (Markoff (or Markov) numbers)". OEIS Foundation. https://oeis.org/A002559. Retrieved 2016-06-17. 
  19. ↑ 19.00 19.01 19.02 19.03 19.04 19.05 19.06 19.07 19.08 19.09 19.10 19.11 19.12 19.13 Sloane, N. J. A., ed. "Sequence A006886 (Kaprekar numbers)". OEIS Foundation. https://oeis.org/A006886. Retrieved 2016-06-17. 
  20. ↑ 20.0 20.1 20.2 Sloane, N. J. A., ed. "Sequence A000014 (Number of series-reduced trees with n nodes)". OEIS Foundation. https://oeis.org/A000014. 
  21. ↑ Sloane, N. J. A., ed. "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". OEIS Foundation. https://oeis.org/A000258. 
  22. ↑ Sloane, N. J. A., ed. "Sequence A000979 (Wagstaff primes)". OEIS Foundation. https://oeis.org/A000979. Retrieved 2016-06-17. 
  23. ↑ 23.0 23.1 23.2 Sloane, N. J. A., ed. "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". OEIS Foundation. https://oeis.org/A000011. 
  24. ↑ 24.0 24.1 24.2 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)". OEIS Foundation. https://oeis.org/A000013. 
  25. ↑ Sloane, N. J. A., ed. "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". OEIS Foundation. https://oeis.org/A000112. 
  26. ↑ 26.0 26.1 Sloane, N. J. A., ed. "Sequence A000129 (Pell numbers)". OEIS Foundation. https://oeis.org/A000129. Retrieved 2016-06-17. 
  27. ↑ 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)". OEIS Foundation. https://oeis.org/A111441. Retrieved 2022-06-02. 
  28. ↑ 28.0 28.1 Sloane, N. J. A., ed. "Sequence A000108 (Catalan numbers)". OEIS Foundation. https://oeis.org/A000108. Retrieved 2016-06-17. 
  29. ↑ Collins, Julia (2019). Numbers in Minutes. United Kingdom: Quercus. pp. 140. ISBN 978-1635061772. 
  30. ↑ Sloane, N. J. A., ed. "Sequence A143641 (Odd prime-proof numbers not ending in 5)". OEIS Foundation. https://oeis.org/A143641. 
  31. ↑ "Sloane's A049384 : a(0)=1, a(n+1) = (n+1)^a(n)access-date=2016-06-17". https://oeis.org/A049384. 
  32. ↑ Sloane, N. J. A., ed. "Sequence A019279 (Superperfect numbers)". OEIS Foundation. https://oeis.org/A019279. Retrieved 2016-06-17. 
  33. ↑ Sloane, N. J. A., ed. "Sequence A065577 (Number of Goldbach partitions of 10^n)". OEIS Foundation. https://oeis.org/A065577. Retrieved 2023-08-31. 
  34. ↑ Weißstein, Eric W. (25 December 2020). "Weakly Prime". https://mathworld.wolfram.com/WeaklyPrime.html. 
  35. ↑ 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)". OEIS Foundation. https://oeis.org/A000957. Retrieved 2022-06-01. 
  36. ↑ Sloane, N. J. A., ed. "Sequence A005165 (Alternating factorials)". OEIS Foundation. https://oeis.org/A005165. Retrieved 2016-06-17. 
  37. ↑ Sloane, N. J. A., ed. "Sequence A040017 (Unique period primes)". OEIS Foundation. https://oeis.org/A040017. Retrieved 2016-06-17. 
  38. ↑ "A007506 - OEIS". https://oeis.org/A007506. 
  39. ↑ "Applesoft Disassembly -- S.d912". http://www.txbobsc.com/scsc/scdocumentor/D912.html.  Disassembled ROM. See comments at $DA1E.
  40. ↑ Sloane, N. J. A., ed. "Sequence A101036 (Riesel numbers)". OEIS Foundation. https://oeis.org/A101036. Retrieved 2016-06-17. 
  41. ↑ Sloane, N. J. A., ed. "Sequence A002110 (Primorial numbers)". OEIS Foundation. https://oeis.org/A002110. Retrieved 2016-06-17. 
  42. ↑ Sloane, N. J. A., ed. "Sequence A005478 (Prime Fibonacci numbers)". OEIS Foundation. https://oeis.org/A005478. Retrieved 2016-06-17. 
  43. ↑ Sloane, N. J. A., ed. "Sequence A006879 (Number of primes with n digits.)". OEIS Foundation. https://oeis.org/A006879. 
  44. ↑ Sloane, N. J. A., ed. "Sequence A002201 (Superior highly composite numbers)". OEIS Foundation. https://oeis.org/A002201. Retrieved 2016-06-17. 
  45. ↑ Sloane, N. J. A., ed. "Sequence A004490 (Colossally abundant numbers)". OEIS Foundation. https://oeis.org/A004490. Retrieved 2016-06-17. 
  46. ↑ Sloane, N. J. A., ed. "Sequence A186509 (Centuries containing 17 primes)". OEIS Foundation. https://oeis.org/A186509. Retrieved 2023-06-16. 
  47. ↑ Sloane, N. J. A., ed. "Sequence A186311 (Least century 100k to 100k+99 with exactly n primes)". OEIS Foundation. https://oeis.org/A186311. Retrieved 2023-06-16. 
  48. ↑ "Dividing one by 998001 produces list of three digit numbers". 23 January 2012. https://www.themarysue.com/one-divided-by-998001/. 
  49. ↑ "Sloane's A002182 : Highly composite numbers". OEIS Foundation. https://oeis.org/A002182. 
  50. ↑ Caldwell, Chris K.. "The Nth Prime Page". https://primes.utm.edu/nthprime/. 
    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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