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The smallest number which is the sum of two distinct odd primes in three ways, i.e., 24 = 5 + 19 = 7 + 17 = 11 + 13. [McCranie] All even numbers up to 24 are expressible as an algebraic sum of the first six odd primes. [Rivera] 24^{250} * 250^{24} + 1 and 24^{125} * 125^{24}  1 are primes. [Kulsha] 24 divides the difference between any two prime squares greater than three. [Walser] There is no prime in which the mean gap between the first n successive primes is exactly 24. [Dodson] In base 24, the square of any number relatively prime to the base (i.e., in this case, any number not divisible by 2 or 3) will end in the digit "1", and 24 is the largest base having this property. [Kerby] 24 divides p^21 for any prime greater than three. [Hockney] The twentyfourth Fermat number (2^2^24 + 1) is composite. [Crandall , Mayer and Papadopoulos] 24 is the largest number less than a thousand such that if it is raised to the sum of its digits plus the sum of its digits, plus and minus one, the results are twin primes. I.e., 24^(2+4)+(2+4) ± 1 are twin primes. [Opao] The atomic numbers (protonelectron pairs) of 24 of the naturally occurring (Hydrogen through Uranium) elements from the periodic table are prime. Coincidentally, 24 of the naturally occurring elements have a prime number of nucleons (protons and neutrons). [Welch] (24!)^2 + 1 is prime. [Patterson] The 24th prime number is 89. The sum of the first 24 prime numbers is 963. Note that 89 mod 24, 963 mod 24, 963 mod 89, 963 mod (89 + 24), 963 mod (89  24), 963 mod (89 mod 24), and the sum of the prime factors of 963 are all prime! [Ranta] (24) = (2!)*(4!). [Firoozbakht] prime(1)^prime(1) + prime(2)^prime(2) + ... + prime(24)^prime(24) is prime. The next such prime (if it exists) has more than 46000 digits. [Firoozbakht] The largest known natural number n such that: prime(n+1)  prime(n) = φ(n). Note that prime(φ(24)+1)  prime(φ(24)) = φ(φ(24)). [Capelle] If the fraction 4/n is not equal to a sum of three distinct unit fractions, then each prime divisor of n must be congruent to 1 modulo 24. [Post] 24*24+2424 plus/minus one are twin primes. [Silva] Exactly half, 24 of the contiguous 48 states of the United States plus the District of Columbia (DC) are adjacent to a prime number of other states or districts. DC, FL, RI, SC, WA are connected to 2 other states; CA, CT, DE, LA, MI, ND, NH, NJ, VT are connected to 3 other states; GA, IL, MA, MD, NV, NY, OH, UT, WV are connected to 5 other states; KY is connected to 7 other states. [Post] There are no known examples of constellations with 24 primes. [Anderson] The largest number of primes that can be found on the Tetractys Puzzle. The smallest nonsphenic number with exactly eight divisors.
(There are 7 curios for this number that have not yet been approved by an editor.)
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