Gematria Primus

What the Gematria Primus is

A table of 29 runes, each paired with a Latin letter or digraph and with a prime number, in a fixed order from ᚠ (F, 2) to ᛠ (EA, 109). It is the key to the readable pages of the Liber Primus, the rune-written book at the centre of the 2014 Cicada 3301 puzzle.

Cicada 3301 was a series of elaborate anonymous puzzles posted in January 2012, 2013 and 2014, ostensibly to recruit “highly intelligent individuals”, that led solvers through image steganography, book ciphers, telephone numbers, physical posters on several continents and a great deal of number theory. Its authors and purpose have never been identified^{[1] Source: Cicada 3301}. The 2014 round ended in the Liber Primus (“First Book”), 58 pages of text written in runes, of which only a few have been deciphered^{[2] Source: Liber Primus}. The Gematria Primus was published inside the puzzle as the rune key; the values are consistent across every deciphered page and are the table used by every solver.

The full table

The runes are the Anglo-Saxon futhorc, an extension of the older Germanic rune-row that added characters for sounds like oe, ae, ea and ia^{[3] Source: Anglo-Saxon runes}. The Primus keeps the traditional rune order and assigns the n-th prime to the n-th rune. The 29 primes sum to 1480.

The index column matters: many Liber Primus pages are not plain transliteration but shifts of the rune indices — each rune moved forward or back by a key, in the manner of a Vigenère cipher — and the prime values are used for sums and checks rather than for the shifting. Where a page uses the Primus directly, reading it is a matter of substitution.

How a word is valued

Transliterate the Latin word into runes, digraphs first, then add the primes. The site does this at build time for the examples below; note that transliteration is where all the ambiguity lives — T-H is one rune (ᚦ, 5), not two (ᛏ + ᚻ, 82), and I-A can be one (ᛡ, 107) or two — so the value of an English word in the Primus depends on choices the table does not make for you.

The Liber Primus

The book is 58 pages of runic text with illustrations, released as images during the 2014 puzzle. Its opening pages — a warning, a passage on “some wisdom”, a parable — were deciphered quickly because they use the Primus with simple keys. The bulk of the book has resisted every attack since, despite a decade of organised effort by a solving community that has tried shifts, running keys, transpositions and statistical analysis^{[2] Source: Liber Primus}. The deciphered portions read as a mystical-philosophical text about self-knowledge and the “divinity within”, written in a deliberately archaic register. Whether the remaining pages are meaningful, a one-time pad, or noise is not known.

Gematria in name only

Gematria — Hebrew, Greek or English — is built on the fact that many words share a sum. Its whole use, from the Talmud to the modern decoder, is to notice that two words land on the same number and to ask what that might suggest^{[5] Source: Gematria}. Greek isopsephy riddles work because a number has many solutions^{[4] Source: Isopsephy}.

The Gematria Primus is designed against that. Prime values make each sum unusually informative about its parts — a multiset of primes has a unique product, and sums of distinct primes collide far less than sums of the small integers 1–26 — and the table exists to encode, verify and unlock text, not to find resonances in it. Cicada borrowed the word because letter-values were involved and because the puzzle enjoyed the esoteric register; the practice it named is the opposite of the one the word describes. This is why the Primus is documented here as an article and not offered as one of the site’s fourteen ciphers: it is a cipher in the cryptographer’s sense, and putting it in a list next to Mispar Hechrachi would misdescribe both.

Curiosities

• 3301 is prime, and so is 1033, its digits reversed; the puzzle’s number is an emirp, which was surely deliberate.
• The 29 primes of the table sum to 1480 — which happens to be the isopsephy of Χριστός (1480) in Greek. This is a coincidence, and a useful one: it is exactly the kind of match gematria is made of, and it means nothing, which is the lesson of the accuracy page in one line.
• Because the values are primes, no two different multisets of runes have the same product. Sums can still collide; products cannot. Nothing in the puzzle is known to exploit this, but it is the property a cryptographer would reach for.
• The futhorc order the Primus uses is the traditional one, which is why F, U, TH, O, R, C are the first six runes — the “futhorc” of the name.