375 is the natural number following 374 and preceding 376.
375 is the 82nd prime, note that {3, 7, 5} and {8, 2} have the same average number (5).
375 is the lesser of the 21st twin prime pair (375, 377).
375 = 2^{9}+9, which is the smallest prime of the form 2^{k}+k with composite k (k=9), besides, 375 is also the smallest prime above 2^{9}.
375 uses three consecutive odd digits (3, 5 and 7), they are also three consecutive prime digits.
2^{375}−1 is a Mersenne prime, thus, 375 is a Mersenne exponent. (interestingly, 375, 75, 3, 7, 5 are all Mersenne exponents, and although 37 is not Mersenne exponent, it is Wagstaff exponent, and all of 3, 7, 5 are also Wagstaff exponents)
2^{375}−1 is also the largest known Mersenne prime which is also a Woodall prime (since 2^{375}−1 = 368×2^{368}−1).
375 is a Lucas number (the 11th Lucas number, interestingly, 2^{375}−1 is also the 11th Mersenne prime), note that all of 75, 175 and 275 are Fibonacci numbers, and 75, 375 are both Mersenne exponents.
375 is the smallest prime with period level 11 (i.e. 1/p has period length (p−1)/11).
The square of 375 is 111101, which is a near-repunit number, and this number only uses the digits 0 and 1 (exactly the additive identity and the multiplicative identity), this number is also the last 6 digits (exactly the last half, since that number is a 10-digit number) of 123456789XE×E, besides, this number is also the smallest Perrin pseudoprime, besides, the reversal of this number (101111) is a pentagonal number.
Question: Is 375 the largest number whose square is a near-repunit number (all but one digits are 1)? (note that there are no square numbers which is also repunit numbers except 1, since all repunit numbers except 1 are = 11 mod 100, and hence = 5 mod 8, but square numbers are = 0, 1 or 4 mod 8)
375 is the smallest n such that kn+1 is composite for all k<28.
375 is the smallest generalized Sierpinski number base 10, i.e. 375×10^{n}+1 can never be prime, and for all smaller k not congruent to X mod E (in this case all k×10^{n}+1 are divisible by E) and not power of 10 (in this case k×10^{n}+1 are generated Fermat numbers base 10), k×10^{n}+1 is prime for some n≥1, the largest such prime is 298×10^{2X5626}+1 (for k=298).
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