XORing the 2013 twitter information with 761.mp3 (The Instar Emergence) resulted in Gematria Primus. Outguessing the Gematria Primus file resulted in a bunch of tabs and spaces, which were converted into ASCII to reveal the next step.
Gematria Primus, found during the 2013 puzzle, is an alphabet with 29 runes, each with an English equivalent and a numerical value, The numerical values are consecutive prime numbers in ascending order. The runes themselves are the focal point of the current step, Liber Primus.
The Gematria Primus alphabet is similar to many old futhorc rune alphabets, but is most similar to an old rune poem. Since Gematria Primus is nearly identical to the poem, it seems to be based off of it. A common theory is that 3301 found a prime number-length alphabet and decided to turn that into their alphabet.
3301's inclusion of a value for each rune allows for a function to assign a number to any word. This is simply adding the value of each rune - what we call gematria sum. 3301 has used this gematria sum previously, notably in the count command from the onion terminal and with certain phrases throughout the puzzles. Certain phrases include:
- The Instar Emergence: 761 (reflected in the song's file name of 761.mp3, and in the song's length of 167 seconds)
- Patience is a virtue: 761
- Interconnectedness: 772 (not prime, but 277 is, which is the song's length in seconds)
- one of the solved pages contains words in runes within a square of numbers; gematria summing the words completes a magic square
- more sentences than you would expect in the solved pages gematria sum to prime numbers
Note that an "order and a value" seems to be a reference to Crowley, who mentioned finding an "order and value" of the English language in the Liber AL vel Legis book previously used by 3301.
A tool for gematria summing is CyberChef, which does gematria sum of individual words.