40,000

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

• 41041 = Carmichael number[5]
• 41472 = 3-smooth number, number of reduced trees with 24 nodes[6]
• 41586 = Large Schröder number
• 41616 = triangular square number[7]
• 41835 = Motzkin number[8]
• 41841 = 1/41841 = 0.0000239 is a repeating decimal with period 7

• 42680 = octahedral number[9]
• 42875 = 35³
• 42925 = square pyramidal number

• 43261 = Markov number[10]
• 43380 = number of nets of a dodecahedron
• 43390 = number of primes ${\displaystyle \leq 2^{19}}$.[11]
• 43560 = pentagonal pyramidal number
• 43691 = Wagstaff prime[12]
• 43777 = smallest member of a prime sextuplet

• 44044 = palindrome of 79 after 6 iterations of the "reverse and add" iterative process[13]
• 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[14]
• 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).[15]
• 44944 = palindromic square

• 45360 = highly composite number;[16] smallest number with exactly 100 factors (including one and itself)

• 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[17]
• 46368 = Fibonacci number[18]
• 46656 = 216² = 36³ = 6⁶, 3-smooth number
• 46657 = Carmichael number[5]

• 47058 = primary pseudoperfect number[19]
• 47160 = 10-th derivative of x^x at x=1[20]
• 47321/33461 ≈ √2

• 48629 = number of trees with 17 unlabeled nodes[21]
• 48734 = number of 22-bead necklaces (turning over is allowed) where complements are equivalent[22]

• 49151 = Woodall number[23]
• 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[24]

There are 930 prime numbers between 40000 and 50000.