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+ The smallest prime that contains all of the prime digits.

+ Chinese Emperor Yao began his reign in 2357 B.C. (A famous legend holds that he created the game of Go to improve the intelligence of his son.)

+ 22 + 33 + 55 + 77 is prime. [Papazacharias]

+ Letting A = 1, B = 2, ..., Z = 26, then 2357 is the sum of all the values of the U.S. Presidents' last names from Washington to Coolidge. [Trotter]

+ 2357 is also the sum of consecutive primes in at least two ways: (773 + 787 + 797) and (461 + 463 + 467 + 479 + 487). [Trotter]

+ The smallest number, curiously prime, whose square begins with 4 identical (prime) digits: 2357^2 = 5555449. [Post]

+ Inserting nineteen zeros between the four prime digits of 2357 makes another prime of prime length sixtyone. Note that 23 + 57 = 19 + 61 and also 19 + 4 = 23 as 57 + 4 = 61. [De Geest]

+ Twenty-three fifty-seven (23:57) is the largest "prime time" of day on a 24-hour clock in hours and minutes. [Luhn]

+ 21013 + 31013 + 51013 + 71013 is prime. [Luhn]

+ 219 + 319 + 519 + 719 is prime. [Ngassam]

+ The prime digits united by unities is prime (2131517). [De Geest]

+ 2*3*5*7+2+3+5+7 and 2*3*5*7-2-3-5-7 are both prime. [Poo Sung]

+ 100^n + 10^n - 1 is prime for consecutive primes 2-3-5-7. [Patterson]

+ The product of the primes less than or equal to 2357 is the smallest titanic primorial number.

+ The number of pies used in the shooting of The Great Race (biggest pie throwing scene on film).

+ Oklahoma is the only U.S. state name whose letters in prime positions are all consonants.

+ The fair approximation log 2/3 = log 5/7 between the successive digits of prime 2357 is a direct consequence of the observation that 27 is close to 53. [Beedassy]

+ The number with each prime digit d repeated d times and the whole sandwiched between two blocks of prime 2357, is prime: 2357223335555577777772357. [Beedassy]

+ Replacing each prime digit in 2357 by its complement forms the prime 8753. Note that combining the two primes by interweaving their digits forms another prime: 82735537. [Beedassy]

+ The sum of 2357 and its successive right-truncations (2357 + 235 + 23 + 2 + 0) is prime, and so is the sum of the successive deleted digits (0 + 7 + 5 + 3 + 2). [Beedassy]

+ 2p7 + 3p5 + 5p3 + 7p2 is prime, where pn is the nth prime. [Beedassy]

+ 2357 = 1234 + 1123. Note the first four prime, natural, and Fibonacci numbers. [Silva]

+ The double Mersenne numbers MMp = 2Mp - 1, (where Mp = 2p - 1) are primes only for p = 2, 3, 5, 7. [Beedassy]

+ Adding the prime digits (2, 3, 5, 7) either to all primes with a prime number of distinct prime digits (23, 37, 53, 73, 257, 523) or to all nonprimes with a nonprime number of distinct prime digits (2375, 2537, 2573, 2735, 3275, 3572, 3725, 3752, 5327, 5372, 5723, 5732, 7235, 7325, 7352, 7532 ) forms a prime in each case (983 ; 76159) the reversal of whose product is also prime (79246847). [Beedassy]

+ 2357 can be expressed as the repdigit sum of its (prime) digits: 2222 + 3 + 55 + 77. Note that the latter summands concatenate, in some appropriate order, into a prime, in three different ways all starting with "55": 553222277, 552222773, 557722223. [Beedassy]

+ The alternating product-series 235*7 +/- 23*57 -/+ 2*357 +/- 23*5*7 -/+ 2*35*7 +/- 2*3*57 -/+ 2*3*5*7 yield prime sums (2689, 601) whose concatenations (2689601, 6012689) are also prime. [Beedassy]

+ The reverse concatenation of the two prime derangements (5273 and 7523) of 2357 is prime: 75235273. Note that sandwiching the latter between two blocks of prime 2357, followed by halving at the middle yields a new pair of primes (23577523 ; 52732357 ) both remaining prime when every digit is replaced by its respective complement (87533587 ; 58378753). [Beedassy]

+ Replacing from the left the first digits in 2357 by their partial sums forms a succession of four primes,viz., 2357, 557, 107, 17. Note that the reversals of both semiprimes 2357*557 and 107*17 are prime (9482131, 9181). [Beedassy]

+ The sum of the cubes of the first four Fibonacci primes. Curiously, the prime contains three of them. [Silva]

+ On the night of 11/13/1991, the Virginia Lottery Pick 4 winning numbers were 2, 3, 5, 7.

(There are 3 curios for this number that have not yet been approved by an editor.)




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