I only recently came across the Cicada 3301 mystery, and curiosity drove me to explore it further and share my findings.
I must have lived in a cave for the last three years, because it appears that the group's riddles became an Internet sensation as early as January 2012 up until 2014, after the last of the known cryptic puzzles was posted. For the benefit of my fellow cave dwellers, allow me to summarize: Cicada 3001 is an unidentified individual, or more likely group of individuals, which released cryptographic challenges online at the rate of one per year for the self-proclaimed purpose of sourcing "highly intelligent individuals" to join their ranks.
In that regard, the method is not groundbreaking; organizations such as the U.S. Cyber Command and the British GCHQ have launched similar initiatives as early as in 2010 to scout individuals with strong analytical capabilities. But in those cases, the recruiter made a point to identify itself so that foreign nationals, who are by definition barred from joining, wouldn't participate. This leads me to believe that Cicada 3301 is not likely to be aligned to any particular national interest (that and the fact that they posted physical clues in different countries).
My interest, however, is not so much in solving the riddles themselves; they have been either solved, or discontinued by their creator to the point that some of the online clues are no longer available. As much as I enjoy challenges of cryptanalysis and logic, this ship has sailed, and Cicada 3301 is not known to have released any new challenge since 2015. Rather, what piqued my curiosity was the opportunity to figure out the identity of the group behind this series of riddles. While I have not figured out who they are, I believe I have uncovered connections that were not found by anyone else (as far as I could tell), and deemed them worthy of sharing here.
While most forum participants (whether on /r/cicada subreddit, or the dedicated wiki) have focused their efforts on solving the cryptographic challenges, I turned my attention to the primodial clue - the name of the group itself. We know that this is a group with more than a passing interest for cryptography, logic, maths, and possibly privacy, freethinking and hermeticism. What can the juxtaposition of the name Cicada and the number 3301 tell us in light of this?
A quick online search turned up a fascinating fact. Periodical cicadas, which include the wonderfully-named Magicicadas in North America, have the rather rare (if not unique) property within the animal kingdom of having a brooding cycle and lifespan set to exactly two prime numbers (13 and 17 years), depending on the species. This is believed to stem from an evolutionary strategy to either reduce the likelihood of pupating alongside predators that have a non-prime cycle (using the mathematical property that primes are not divisible by any other number but 1 and themselves), or to avoid hybridization between the two species (since the only common brooding year would reoccur every 13 x 17 = 221 years), or both.
For a group so fond of cryptography, it is difficult to think of a more suitable mascot than an animal whose very existence is regimented by prime numbers. Indeed, large primes (typically of 1,024 to 4,096 bits in length) have formed the backbone of some assymetric (public-key) cryptographic algorithms (such as RSA) since the 1970s. The strength of these algorithms relies on the computational inefficiency of factoring the product of two large primes (at least on non-quantum computers - it would pave the way for the mother of all hacks if an efficient quantum algorithm for this was ever devised).
Having settled on a likely reason for the choice of "Cicada" in the name (at least for now - more on this later), let's turn our attention to the number 3301. It is, obviously, a prime number; which reinforces the assumption that cryptography, and the privacy it has to offer, is core to the group's values. But why this particular prime? After all, Euclid proved in 300 BC that there is an infinite set of primes, so we must look deeper into the conscious decision that was made of picking this particular prime over others, such as 13 or 17 for instance. A quick test that comes to mind is the prime-counting function n = pi(P), which gives us the position n of a prime number P within the sequence of primes (a.k.a. sequence A000040). Plugging this into Wolfram Alpha with a prime value of P = 3301 returns the number 464.
The first thing that came to my mind, amusingly enough, is the Amstrad CPC 464 - the 8-bit, 64KB-RAM, cassette-tape computer on which many Gen-X children took their first programming steps in Locomotive BASIC during the second half of the 1980s. I pictured for a moment the Cicada 3301 group being comprised of hackers in their late thirties reminiscing about the pioneering days of personal computing and hiding a tongue-in-cheek allusion in the name of their organization. But somehow this felt childish and overly trivial, relative to the amount of effort and intelligence displayed in the design of the cryptographic challenges. There had to be more to it than just geeky memories of playing Paperboy on a 27-color CRT screen.
My second observation was that 464 is a primitive abundant number, which means that the sum of its divisors (1+2+4+8+16+29+58+116+232=466) is greater than the number itself, and the sum of the divisors of each divisor is smaller than that divisor itself. It is also the 8th such number in the sequence of primitive abundant numbers, or the 33th in the sequence of abundant numbers that have no abundant proper divisor. Interesting mathematical trivia perhaps, but a dead end in my view.
I then thought of the group's first public appearance in 2012. It is not unreasonable to speculate that the number 3301, and more to the point its prime count of 464, is a relative reference to the date of the group's first outing. A quick substraction of 464 from the year 2012 gives us 1548. What happened that year? I went through a Wikipedia list of relatively obscure events, births and dates from that year and was unconvinced - until I noticed that it was the birth year of Giordano Bruno.
The great man should not warrant an introduction, but to be safe, I'll summarize his oustanding credentials briefly, at the risk of not doing him justice: a philosopher, poet, cosmologist, hermeticist and scholar, Bruno was a freethinking polymath and an enlightened secular humanist of the Italian Rinascimento. Among his stunning achievements, he first postulated that stars in the night sky are suns similar to ours, that there is an infinite number of solar systems and galaxies, and that alien life is likely. Those ideas, among others, displeased the Church - but unlike his spiritual successor Galileo, Bruno did not recant and was burnt at the stake in Rome in 1600. His interests in hermeticism and the geometry of language seem to resonate well with those of Cicada 3301. But this connection was circumstancial at best.
Or so I thought, until I read more about Bruno's early years (emphasis added):
Bruno gives in his greatest Latin work, the De immenso, a description of an episode in childhood, which made a deep impression on him. His home was in a hamlet just outside Nola, on the lower slopes of Cicada, a foot-hill of the Appenines some twenty miles east of Naples. He tells with affectionate detail of the beauty and fertility of the land around, overlooked from afar by the seemingly stern bare steeps of Vesuvius. One day a suspicion of the deceptiveness of appearances dawned on the boy. Mount Cicada, he tells us, assured him that "brother Vesuvius" was no less beautiful and fertile. So, girding his loins, he climbed the opposite mountain. "Look now," said Brother Vesuvius, "look at Brother Cicada, dark and drear against the sky." The boy assured Vesuvius that such also was his appearance viewed from Cicada. "Thus did his parents [the two mountains] first teach the lad to doubt, and revealed to him how distance changes the face of things." So in after-life he interprets the experience and continues: "In whatever region of the globe I may be, I shall realize that both time and place are similarly distant from me." The incident gives the impression of an adventurous and happy child with a vivid imagination and a mind already active. We see too the germ of creative power and of philosophic insight as well as the element of whimsy.
I kid you not, dear reader; Giordano Bruno's birthplace is on Mount Cicada (Monte Cicala in Italian, topped by a XIIth-century castle named Castelcicala). Bruno gives himself the name "Cicada" as a protagonist in one of his philophical dialogues (De gli eroici furori, 1585).
If I am wrong in my deduction that Cicada 3301 is leading us in the footsteps of Giordano Bruno, then I hope that you, dear reader, will at least concur that the coincidence is quite extraordinary, and will forgive my pareidolia. And if I am right, I am curious to see in what ways Cicada 3301 is bringing Giordano Bruno's legacy to life; for, as the poet wrote,
For to die in one age makes us live in all the rest.
it has been brought to my attention that an alleged Cicada 3301 poster was placed onto Giordano Bruno's statue in Campo di Fiori, Rome (original 4chan thread, archive) in the past few hours. This could either be a hoax from someone who read my post or formulated the same hypothesis independently, or it could be the validation that Cicada 3301 points us to Giordano Bruno and his legacy.