Sum of reciprocals of prime numbers, using alternating sings

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Does the Sum from N=1 to N= of : (-1^(N+1))((1/P(N)), where P(N) is the nth prime number, converge? If so, to what number does it converge?

Or in different terms, does the sum of the reciprocal of primes, where there are alternating signs, converge?

Example: (1/2)-(1/3)+(1/5)-(1/7)+(1/11) . . . = ?