# euler / go / src / euler / 27.go

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60``` ```/* Euler published the remarkable quadratic formula: n² + n + 41 It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly divisible by 41. Using computers, the incredible formula n² 79n + 1601 was discovered, which produces 80 primes for the consecutive values n = 0 to 79. The product of the coefficients, 79 and 1601, is 126479. Considering quadratics of the form: n² + an + b, where |a| 1000 and |b| 1000 where |n| is the modulus/absolute value of n e.g. |11| = 11 and |4| = 4 Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0. Answer: -59231 */ package main import ( "fmt" ) func e27() { best_a, best_b, best_n := 0, 0, 0 for a := -999; a < 1000; a++ { for b := -999; b < 1000; b++ { n := 0 for { v := n*n + a*n + b if v < 0 { break } if !IsPrime(uint64(v)) { break } n++ } if n > best_n { best_a, best_b, best_n = a, b, n } } } fmt.Println(best_a * best_b) } func init() { register("27", e27) } ```