Naive take on this math problem: http://math.stackexchange.com/q/597234

p38n31.go

package main

import (
	"math/big"
	"fmt"
)

type powersOf struct {
	E int64
	b, n *big.Int
}

func newPowersOf(n int64) *powersOf {
	return &powersOf{
		b: big.NewInt(1),
		n: big.NewInt(n),
	}
}

func (p *powersOf) Next() *big.Int {
	p.E++
	p.b = p.b.Mul(p.b, p.n)
	return p.b
}

func main() {
	var x *big.Int
	p := newPowersOf(38)
	q := big.NewInt(31)
	for {
		x = p.Next()
		// http://math.stackexchange.com/q/597234#comment1258402_597234
		if (p.E%12 != 0) && (p.E%12 != 8) {
			continue
		}
		// http://math.stackexchange.com/q/597234#comment1447435_597234
		if p.E < 185000 {
			continue
		}

		fmt.Printf("\rn=%d, bitlen=%d", p.E, x.BitLen())

		if x.Add(x, q).ProbablyPrime(8) {
			fmt.Printf("\nPRIME(8) for n=%d\n", p.E)
			break
		}
		x.Sub(x, q)
	}
}