From c4c2ae138bf6af69b06c64bcc23ae1d556e44de7 Mon Sep 17 00:00:00 2001
From: daviddoji <daviddoji@pm.me>
Date: Sat, 25 Sep 2021 19:47:37 +0200
Subject: [PATCH] Solution to problem 51 in Julia

---
 src/Julia/Problem051.jl | 69 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 69 insertions(+)
 create mode 100644 src/Julia/Problem051.jl

diff --git a/src/Julia/Problem051.jl b/src/Julia/Problem051.jl
new file mode 100644
index 0000000..1bf70ec
--- /dev/null
+++ b/src/Julia/Problem051.jl
@@ -0,0 +1,69 @@
+#=
+Created on 25 Sep 2021
+
+@author: David Doblas Jiménez
+@email: daviddoji@pm.me
+
+Solution for Problem 51 of Project Euler
+https://projecteuler.net/problem=51
+=#
+
+using BenchmarkTools
+using Primes
+
+function Problem51()
+    #=
+    By replacing the 1st digit of the 2-digit number *3, it turns out that
+    six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.
+
+    By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit
+    number is the first example having seven primes among the ten generated numbers,
+    yielding the family:
+
+        56003, 56113, 56333, 56443, 56663, 56773, and 56993.
+
+    Consequently 56003, being the first member of this family, is the smallest prime
+    with this property.
+
+    Find the smallest prime which, by replacing part of the number (not necessarily
+    adjacent digits) with the same digit, is part of an eight prime value family.
+    =#
+
+    primes_list = primes(57_000,1_000_000)
+    digits = Dict('0'=>[], '1'=>[], '2'=>[],'3'=>[], '4'=>[], '5'=>[], '6'=>[], '7'=>[], '8'=>[], '9'=>[])
+    for d in keys(digits)
+        for p in primes_list
+            p_ = string(p)
+            dummy = string(d)
+            if length(collect(eachmatch(Regex(dummy), p_))) == 3 && p_[end] != string(d)
+                push!(digits[d],p)
+            end
+        end
+    end
+    for d in ['0', '1', '2']
+        for p in digits[d]
+            res = 0
+            i = 10
+            dummy = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
+            for D in deleteat!(dummy, findall(x->x==d, dummy))
+                i -= 1
+                q = parse(Int, replace(string(p), d=>D))
+                if isprime(q) && q > 57_000
+                    res += 1
+                end
+                if i + res < 7
+                    break
+                end
+            end
+            if res == 7
+                return p
+            end
+        end
+    end
+end
+
+
+println("Time to evaluate Problem 51:")
+@btime Problem51()
+println("")
+println("Result for Problem 51: ", Problem51())