30,000 Explained

30,000 (thirty thousand) is the natural number that comes after 29,999 and before 30,001.

Selected numbers in the range 30001–39999

30001 to 30999

• 30029 = primorial prime
• 30030 = primorial
• 30031 = smallest composite number which is one more than a primorial
• 30203 = safe prime
• 30240 = harmonic divisor number
• 30323 = Sophie Germain prime and safe prime
• 30420 = pentagonal pyramidal number
• 30537 = Riordan number
• 30694 = open meandric number
• 30941 = first base 13 repunit prime

31000 to 31999

• 31116 = octahedral number
• 31185 = number of partitions of 39
• 31337 = cousin prime, pronounced elite, an alternate way to spell 1337, an obfuscated alphabet made with numbers and punctuation, known and used in the gamer, hacker, and BBS cultures.
• 31395 = square pyramidal number
• 31397 = prime number followed by a record prime gap of 72, the first greater than 52
• 31688 = the number of years approximately equal to 1 trillion seconds
• 31721 = start of a prime quadruplet
• 31929 = Zeisel number

32000 to 32999

• 32043 = smallest number whose square is pandigital.
• 32045 = can be expressed as a sum of two squares in more ways than any smaller number.
• 32760 = harmonic divisor number
• 32761 = 181², centered hexagonal number
• 32767 = 2¹⁵ - 1, largest positive value for a signed (two's complement) 16-bit integer on a computer.
• 32768 = 2¹⁵ = 8⁵ = 32³, maximum absolute value of a negative value for a signed (two's complement) 16-bit integer on a computer.
• 32800 = pentagonal pyramidal number
• 32993 = Leyland number

33000 to 33999

• 33333 = repdigit
• 33461 = Pell number, Markov number
• 33511 = square pyramidal number
• 33781 = octahedral number

34000 to 34999

• 34560 = 5 superfactorial
• 34790 = number of non-isomorphic set-systems of weight 13.
• 34841 = start of a prime quadruplet
• 34969 = favorite number of the Muppet character Count von Count^[1]

35000 to 35999

• 35720 = square pyramidal number
• 35840 = number of ounces in a long ton (2,240 pounds)
• 35890 = tribonacci number
• 35899 = alternating factorial
• 35937 = 33³, chiliagonal number
• 35964 = digit-reassembly number

36000 to 36999

• 36100 = sum of the cubes of the first 19 positive integers
• 36463 – number of parallelogram polyominoes with 14 cells
• 36594 = octahedral number

37000 to 37999

• 37338 = number of partitions of 40
• 37378 = semi-meandric number^[2]
• 37634 = third term of the Lucas–Lehmer sequence
• 37666 = Markov number
• 37926 = pentagonal pyramidal number

38000 to 38999

• 38024 = square pyramidal number
• 38209 = n such that n | (3ⁿ + 5)
• 38305 = the largest Forges-compatible number (for index 32) to the field

Q (\sqrt{ 6 }, \sqrt{ 14 }) . But a conjecture of Viggo Brun predicts that there are infinitely many such numbers for any Galois field F unless F is bad.

• 38416 = 14⁴
• 38501 = 7⁴ + 190²: Friedlander-Iwaniec prime. Smallest prime separated by at least 40 from the nearest primes (38461 and 38543). It is thus an isolated prime. Chen prime.
• 38807 = number of non-equivalent ways of expressing 10,000,000 as the sum of two prime numbers^[3]
• 38962 = Kaprekar number

39000 to 39999

• 39299 = Integer connected with coefficients in expansion of Weierstrass P-function
• 39304 = 34³
• 39559 = octahedral number
• 39648 = tetranacci number

Primes

There are 958 prime numbers between 30000 and 40000.

Notes and References

1. Web site: Why was 34,969 Count von Count's magic number?. 2012-08-30. 2012-08-31. BBC News.
2. Web site: Sloane's A000682 : Semimeanders. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
3. A065577. Number of Goldbach partitions of 10^n. 2023-08-31.