# The Mystery of Primes

Number Theory Level pending

let the series $$a_1,a_2,a_3,a_4 ...$$ , be the series of prime numbers starting with 3.

What will be that value of the infinite series (1 ■ $$\frac{1}{a_1}$$)(1 ■ $$\frac{1}{a_2}$$)(1 ■ $$\frac{1}{a_3}$$)... given these rules

You must fill the black square with the appropriate sign according to these rules:

1) if the value of $$a_n$$ can be represented by 4k+1 where k is a positive integer, replace the black box with a PLUS sign

2) if not then replace the black box with a MINUS sign

Shown below are the first 3 terms of the infinite series (1-$$\frac{1}{3}$$)(1+$$\frac{1}{5}$$)(1-$$\frac{1}{7}$$)

The value of the infinite series (1 ■ $$\frac{1}{a_1}$$)(1 ■ $$\frac{1}{a_2}$$)(1 ■ $$\frac{1}{a_3}$$)... can be represented as $$\frac{x}{y}$$ where x and y are real numbers and $$\frac{x}{y}$$ is in lowest terms. What is the value of [x+y]?

[x] represents the greatest integer function.

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