- Sep 4, 2001This post is about the Wieferich primes, 1093 and
(1) Concerning the two in concert producing a prime P
(2) Concerning what I have found to be an interesting
composite for P+1 and possibilities for primes close
(3) Concerning 3511 itself, a Wieferich prime.
(1) Let f(x,y) = x^2 - y^2 -2xy.
f(3511,1093) = 7294949 and is prime P.
(2) 7294950 = 2*3*3*5*5*13*29*43 which made it easy to
factorise into its 8 factors, of which 5 are less than
(P+1)^(1/8) and all less than (P+1)^(1/4). This fact
seem to me to make 7294950 fairly interesting as only
6435 previous composites have the property of having 8
prime factors, one in more than a thousand.
(3) f(79,26) = 3511 itself remarkable as 79 = 3*26+1
which makes it a "near" Lucas series with its
characteristic second term 79 = 1mod3 and 1mod(the
first term viz. 26 in this case).
(I have postulated that any prime 1mod10 or -1mod10 is
always expressible with x > 3y in f(x,y), and that x
is the second term of a Fibonacci series T(1) = y,
T(2) = x.)
I have more interesting material but unless this
creates interest, I will spare you it.
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