For the curious: the reason that this property with 24 holds is because 24 = 2^3 * 3. For any prime number p:

p^2 - 1 = (p+1)(p-1)

And p+1 and p-1 must both be multiples of 2 because p is odd. Furthermore, one of p+1 or p-1 is also a multiple of 4 (because they are both multiples of 2 and only 2 apart). So, we can see where the 2^3 factor comes from in the magic number 24. The remaining factor, 3, comes from the fact that p is prime and not a multiple of 3, so either p+1 or p-1 must be a multiple of 3 (otherwise p-1, p, and p+1 would be three consecutive numbers, none of which are divisible by 3, which is impossible).

As a result, for any prime p > 3, (p+1)(p-1) is divisible by 24, so p^2 - 1 is also divisible by 24.

The BBC obituary on Shulgin[1] calls him the "Godfather of Ecstasy"[2], but he was far more than that.

He synthesized and carefully chronicled the effects of hundreds of psychoactive compounds on himself and a small, dedicated core group of explorers of human consciousness.

His efforts were published in two massive, definitive tomes called PiHKAL[3][4] and TiKHAL[5][6], the titles of which stand for "Phenethylamines I Have Known and Loved" and "Tryptamines I Have Known and Loved", respectively.

These volumes contained detailed chemical synthesis instructions for the compounds he created, along with "trip reports" and ratings[7] of the compounds' psychoactivity, ranging from:

PLUS / MINUS (+/-) "The level of effectiveness of a drug that indicates a threshold action. If a higher dosage produces a greater response, then the plus/minus (+/-) was valid. If a higher dosage produces nothing, then this was a false positive."

to

PLUS FOUR (++++) "A rare and precious transcendental state, which has been called a 'peak experience', a 'religious experience,' 'divine transformation,' a 'state of Samadhi' and many other names in other cultures. It is not connected to the +1, +2, and +3 of the measuring of a drug's intensity. It is a state of bliss, a participation mystique, a connectedness with both the interior and exterior universes, which has come about after the ingestion of a psychedelic drug, but which is not necessarily repeatable with a subsequent ingestion of that same drug. If a drug (or technique or process) were ever to be discovered which would consistently produce a plus four experience in all human beings, it is conceivable that it would signal the ultimate evolution, and perhaps the end of, the human experiment."

His chemistry lab was DEA-licensed to handle "illegal" (scheduled) compounds, though he often synthesized entirely novel compounds which were not scheduled because neither the compounds nor the laws scheduling them existed yet.

Shulgin tirelessly educated the public and the law-enforcement community on the effects and value of psychedelic and psychoactive compounds, and wrote a highly informative Q&A column.[7]

Shulgin's pioneering work inspired generations of chemists, self-experimenters, and explorers. He was well known, loved, and respected as one of the most highly accomplished psychedelic chemists in history. His presence and guidance will be deeply missed.

[1] - https://en.wikipedia.org/wiki/Alexander_Shulgin

[2] - http://www.bbc.co.uk/news/health-27676669

[3] - https://en.wikipedia.org/wiki/PIHKAL

[4] - http://www.erowid.org/library/books_online/pihkal/pihkal.sht...

[5] - https://en.wikipedia.org/wiki/TIHKAL

[6] - http://www.erowid.org/library/books_online/tihkal/tihkal.sht...

[7] - http://www.cognitiveliberty.org/shulgin/blg/index.html

I had dinner with him once at a conference; he was amazing. When asked about the safety of self-testing novel substances (he of course starts at insanely low doses, but still), he said that he's learned to identify the signs of grand mal seizures, and if he feels one coming on, he simply sticks himself with a couple hundred miligrams of phenobarbital, straps himself in, and goes for a ride. Then he gets back to work.

Exposing yourself to the direct, harsh feedback of the market is key. I've noticed that bad founders will do just about anything to avoid this. Instead of selling, which is hard, they spend their time going to conferences and meetups, trying to do PR, talking to biz dev people about partnerships, etc. It all sounds like work, but mainly serves to insulate them from the harsh reality that nobody wants their product.