Let the sequence of primes, with 1 adjoined, be denoted by p0 = 1, P1= 2, p2 = 3, p3 = 5,...

Let the sequence of primes, with 1 adjoined, be denoted by p0 = 1, P1= 2, p2 = 3, p3 = 5, …. For each n ≥ 1, it is known that there exists a suitable choice of coefficients ∊k = ± 1 such that

To illustrate:

And

Determine similar representations for the primes 23, 29, 31, and 37.