# Solve

Posted on Jul 21 2019 - 3:10pm

The first thing we notice is that some of the numbers are repeated.

761269 12766547 82039649 53739689 2994919 22579 83683 650729 402733 402733 3048371 3048371 319373 3167371 30232117 3048371 3150487 2037839 22579 364547 2834761 84923 2211421 120569929 7189583 495917 3167371 70100689 20201263 731099 2969077 31244849 6453583 650729 4630127 6869651 625357 1204601 1100371 120457 131867 597851 546121 385019 3048371 51997837 6869651 51791 99763 1859761 27576671 133511713 3150487 631973 743569

That is good, as it indicates there is a pattern to be found.

We also note they are all odd numbers.  We test to see if they are prime numbers.  They are not.

A little more testing and we find out that each of our numbers is the product (multiplication) of two prime numbers.  You can find sites on the Internet that if you plug a number in well tell you its prime factors.  Here is an example of the first few.

 # Number Prime 1 Prime 2 1 761269 = 809 x 941 2 12766547 = 13567 x 941 3 82039649 = 6047 x 13567 4 53739689 = 6047 x 8887

Finish this process for all Numbers.

You wil also notice that one of the prime numbers for each Number matches one of the prime numbers from the previous Number.  Now we really have a pattern going !  Arrange the prime numbers so that Prime 1 is the same as Prime 2 from the last Number.  Your spreadsheet should now start looking like this.

 # Number Prime 1 x Prime 2 1 761269 = 809 x 941 2 12766547 = 941 x 13567 3 82039649 = 13567 x 6047 4 53739689 = 6047 x 8887

You will find there are 20 unique prime numbers that are used to multiply together to create the Numbers we were given in the clue.  This is the start of an alphabet.  List the unique prime numbers from Prime 1 and Prime 2 into table, sort them from lowest to highest, and then assign letters "a" through "t".  You will get something starting like this.

 67 = a 163 = b 337 = c 491 = d

We apply these letters to column Prime 1 and we start getting a phrase "ijsqrc" and so on.  Most of it looks unreadable, but you can start to see words in there.

The last step is to use a "substitution cipher" to clear the letters up into a meaningful phrase.  Google "substitution cipher solver" and you will find some.  You will need to play with them to find out which one works best for you.

Put your text into the solver and you get the phrase "icamehere" .....  There may be a couple words you need to fix or complete. The password is all lowercase and has no spaces.

Congratulations, you have walked through solving this key step by step !