40,000

40001 to 40999

• 40320 = smallest factorial (8!) that is not a highly composite number
• 40425 = square pyramidal number
• 40585 = largest factorion^[1]
• 40678 = pentagonal pyramidal number
• 40755 = the smallest number >1 to be a Triangular number, Pentagonal number, and a Hexagonal number.^[2] Additionally, it's a 390-gonal, 4077-gonal, and 13586-gonal number.^[3][4][5]
• 40804 = palindromic square

41000 to 41999

• 41041 = Carmichael number^[6]
• 41472 = 3-smooth number, number of reduced trees with 24 nodes^[7]
• 41586 = Large Schröder number
• 41616 = triangular square number^[8]
• 41835 = Motzkin number^[9]
• 41841 = 1/41841 = 0.0000239 is a repeating decimal with period 7

42000 to 42999

• 42680 = octahedral number^[10]
• 42875 = 35³
• 42925 = square pyramidal number

43000 to 43999

• 43261 = Markov number^[11]
• 43380 = number of nets of a dodecahedron
• 43390 = number of primes ${\displaystyle \leq 2^{19}}$.^[12]
• 43560 = pentagonal pyramidal number
• 43691 = Wagstaff prime^[13]
• 43777 = smallest member of a prime sextuplet

44000 to 44999

• 44044 = palindrome of 79 after 6 iterations of the "reverse and add" iterative process^[14]
• 44100 = sum of the cubes of the first 20 positive integers 44,100 Hz is a common sampling frequency in digital audio (and is the standard for compact discs).
• 44444 = repdigit
• 44583 = number of partitions of 41^[15]
• 44721 = smallest positive integer such that the expression ⁠1/n⁠ − ⁠1/n + 2⁠ ≤ 10⁻⁹
• 44724 = maximum number of days in which a human being has been verified to live (Jeanne Calment).^[16]
• 44944 = palindromic square

45000 to 45999

• 45360 = 26th highly composite number;^[17] smallest number with exactly 100 factors (including one and itself)

46000 to 46999

• 46080 = double factorial of 12
• 46233 = sum of the first eight factorials
• 46249 = 2nd number that can be written as ${\displaystyle a^{2}+b!}$ in 3 ways^[18]
• 46368 = Fibonacci number^[19]
• 46656 = 216² = 36³ = 6⁶, 3-smooth number
• 46657 = Carmichael number^[6]
• 46972 = number of prime knots with 14 crossings

47000 to 47999

• 47058 = primary pseudoperfect number^[20]
• 47160 = 10-th derivative of x^x at x=1^[21]
• 47321/33461 ≈ √2

48000 to 48999

• 48629 = number of trees with 17 unlabeled nodes^[22]
• 48734 = number of 22-bead necklaces (turning over is allowed) where complements are equivalent^[23]

49000 to 49999

• 49151 = Woodall number^[24]
• 49152 = 3-smooth number
• 49726 = pentagonal pyramidal number
• 49940 = number of 21-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed^[25]

Primes

There are 930 prime numbers between 40000 and 50000.