The number of pairs of twin primes less than 1000.
The first composite number occurring in Pascal's Triangle whose digit reversal is prime.
The product of 35 and 36 has the same prime factors as the product of 4374 and 4375. [Guy]
35 is the smallest product of Twin primes of the form (4*k+1, 4*k+3), k>0. [Zumkeller]
The number of known even numbers which are not the sum of
two twin primes (coming from the same pair or not). [Capelle]
35 can be written as a sum of odd primes in 35 ways, and as a sum of primes in 35 * 5 ways. [Hartley]
35 = 23 + 33, i.e., the sum
of the cubes of the first two primes. [Mizuki]
35 is the smallest number formed from two odd primes. It's prime factors are 5 and 7. Note that its digital sum (8) and digital product (15) are each one less than perfect squares. No prime number greater than 3 fits this category. [Storms]
5*7 = (29+41)/2 is a 2-almost prime (biprime) formed by 2nd
twin prime couple and also arithmetic mean of 2 consecutive
lesser primes of two twin prime couples. Much MORE: (a)
(p,q) = (5,7) and (29,41) are the first two consecutive
prime solutions of Diophantine equation 2*p^2 = 1+q^2, (b)
(p*q)^2 = q^2*(q^2+1)/2, i.e., triangular number T(q^2) a
square, (c) p^2 = [(q-1)/2)]^2+[(q+1)/2]^2, i.e., two
Pythagorean triples (a,b,c) with a prime hypotenuse c = p
and two legs a, b which differ just by 1: b-a =
(q+1)/2-(q-1)/2=1. [Krug]
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