prime_recursive_representation.sf

#!/usr/bin/ruby

# Represent a given prime using only 2s and 1s, recursively using its P +/- 1 factorization.

func pminus1_representation(p) {

    return "2" if (p == 2)

    '(' + (p-1 -> factor_map{|p,e|
        var t = __FUNC__(p)
        e == 1 ? t : "#{t}^#{e}"
    }.join(' * ')) + ' + 1)'
}

func pplus1_representation(p) {

    return "2" if (p == 2)

    '(' + (p+1 -> factor_map{|p,e|
        var t = __FUNC__(p)
        e == 1 ? t : "#{t}^#{e}"
    }.join(' * ')) + ' - 1)'
}

say "=> P-1 representation:"
say pminus1_representation(59649589127497217)

say "\n=> P+1 representation:"
say pplus1_representation(59649589127497217)

__END__
=> P-1 representation:
(2^9 * (2 * (2 * (2 + 1) + 1) * (2^6 * (2 * (2 + 1) + 1) + 1) * (2 * (2 + 1)^3 * (2^2 * (2 + 1)^2 * (2^2 + 1) + 1) * (2^2 * (2 + 1)^2 * (2^6 * (2 * (2 + 1) * (2^3 * (2^4 + 1) + 1) + 1) + 1) + 1) + 1) + 1) + 1)

=> P+1 representation:
(2 * (2^2 - 1) * (2 * (2^4 * (2^3 * (2^2 - 1) - 1) - 1) - 1) * (2^3 * (2^5 - 1) * (2^4 * (2^2 - 1) * (2^3 - 1) * (2 * (2^2 - 1) * (2^2 * (2 * (2^2 - 1) - 1) - 1) - 1) - 1) * (2 * (2^2 - 1) * (2 * (2 * (2^2 - 1)^2 - 1) * (2^3 * (2^2 - 1) - 1) * (2^2 * (2^3 - 1) * (2^2 * (2^2 - 1) - 1) - 1) - 1) - 1) - 1) - 1)