Significance of Even-oddness of a Prime's Penultimate Digit
نویسنده
چکیده
The beauty of these relationships is that, by inspection alone, one may instantly observe whether or not a prime number is = 1, or = 3 (mod 4). These relationships are especially valuable for very large prime numbers-such as the larger Mersenne primes. Thus, it is seen from inspection of the penultimate digits of the Mersenne primes, as given in [1 ] , that all of the given primes are = 3 (mod 4). This holds true for all Mersenne primes, however large they may be, for, by adding and subtracting 4 from Mp= 2 1 and re-arranging, we have Mp 2 1+4-4 = 2 -4 + 3 4(2"1)+3 3 (mod 4).
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