prog.sf

#!/usr/bin/ruby

# Numbers that are the sum of m = 5 successive primes and also the product of m = 5 (other) successive primes.
# https://oeis.org/A323052

var a = [
    2775683761181, 10945513774549181, 31285407706348267, 43861128120750079, 100441814079170659, 159395121707397143, 402260157804827743, 1340537842364790347, 4738876023641493659, 16292356006439865799, 27911122766554363873
]

# 27911122766554363873
# 27911122766554363847
# 27911122766554364033

# 27911122766554363847
# 27911122766554364033

# sum(5582224553310872717, 5582224553310872743, 5582224553310872749, 5582224553310872771, 5582224553310872867)
# sum(5582224553310872743, 5582224553310872749, 5582224553310872771, 5582224553310872867, 5582224553310872903)

func is_sum(n) {

    var k = floor(n/5)

    loop {

        if (k.is_prime) {
            var r = 5.of { k }.map_reduce{|a| a.next_prime }.sum

            if (r < n) {
                #die "not ok: #{n} -- #{k}"
                return false
            }

            if (r == n) {
                #say "#{n} = sum(#{r})";
                #break
                return true
            }
        }

        k.prev_prime!
    }
}

STDOUT.autoflush(1)

for p in (primes(100000)) {
    var n = 5.of { p }.map_reduce{ .next_prime }.prod

    if (is_sum(n)) {
        print(n, ", ")
    }
}

__END__

a.each {|n|
    var f = n.factor
    assert_eq(5.of { f[0] }.map_reduce {|a| a.next_prime }, f)

    var k = floor(n/5)

    loop {

        if (k.is_prime) {
            var r = 5.of { k }.map_reduce{|a| a.next_prime }

            if (r.sum < n) {
                die "not ok: #{n} -- #{k}"
            }

            if (r.sum == n) {
                say "#{n} = sum(#{r})";
                break
            }
        }

        k.prev_prime!
    }
}