1. The smallest RSA number not yet factored is 220 digits. The RSA numbers themselves are useless for this experiment because if one did get the right factors, because it’s so extraordinarily unlikely for machine-elves to really be an independent reality, a positive result would only prove that someone had stolen the RSA answers or hacked a computer or something along the lines. RSA-768 was factored in 2009 using ~2000 CPU-years, so we need a number much larger; since Google has several million CPUs we might want something substantially larger, at least 800 digits. We know from mnemonists that numbers that large can be routinely memorized, and an 800 digit decimal can be memorized in an hour. Chao Lu memorized 67k digits of Pi in 1 year. So the actual memorization time is not significant. How much training does it take to memorize 800 digits? I remember a famous example in WM research of how WM training does not necessarily transfer to anything, of a student taught to memorize digits, Ericsson & Chase’s whose digit span went from ~7 to ~80 after 230 hours of training; digit span is much more demanding than a one-off memorization. This does something similar using more like 80 hours of training. Foer’s _Moonwalking With Einstein: The Art and Science of Remembering Everything_ doesn’t cover much more than a year or two and fairly undemanding training regimen, and he performed well. So I’m going to guess that to memorize a number which would be truly impressive evidence (and not simply evidence for a prank or misdeeds by a hobbyist, RSA employee, Google, or the NSA) would require ~30h of practice.
2. some browsing of the DMT category on the current leading black-market suggests that 1g of DMT from a reputable seller costs ฿0.56 or ~$130. The linked paper says smoking DMT for a full trip requires 50mg/0.05g so our $130 buys ~19 doses.
3. The linked paper says that 20% of Strassman’s injected-DMT trips give a machine-elf experience; hence the 1g will give an average of ~3-4 machine-elfs and 19 trips almost guarantees at least 1 machine-elf assuming 20% success-rate (1-(1-0.2)^19 = 98%). Since the 20% figure comes from injected DMT and DMT of a controlled high quality, probably this is optimistic for anyone trying out smoking DMT at home, but let’s roll with it.
4. in a machine-elf experience, how often could we be lucid enough to wake up and ask the factoring question? No one’s mentioned trying so there’s no hard data, but we can borrow from a similar set of experiments in verifying altered states of consciousness, Laberge’s lucid dreaming experiments in which subjects had to exert control to wiggle their eyes in a fixed pattern. This study gives several flows from # of nights to # of verifications, which all are roughly 1/3 – 1/4; so given our estimated 3-4 machine-elfs, we might be able to ask 1 time. If the machine-elves are guaranteed to reply correctly, then that’s all we need.
5. at 30 hours of mnemonic labor valued at minimum wage of $8 and $130 for 19 doses, that gives us an estimate of $370 in costs to ask an average of once; if we amortize the memorization costs some more by buying 2g, then we instead spend $250 per factoring request for 2 tries; and so on down to a minimum cost of (130/19)*5 = $34 per factoring request. To get n=10 requests, we’d need to spend a cool ((30*8) + 10*130)=$1540.
6. power analysis for a question like this is tricky, since we only need one response with the *right* factors; probably what will happen is that the machine-elfs will not answer or any answer will be ‘forgotten’. You can estimate other stuff like how likely the elves are to respond given 10 questions and 0 responses (flat prior’s 95% CI: 0-28%), or apply decision-theory to decide when to stop trying (tricky, since any reasonable estimate of the probability of machine-elves will tell you that at $35 a shot, you shouldn’t be trying at all).

Hence, you could get a few attempts at somewhere under $1k, but exactly how much depends sensitively on what fraction of trips you get elves and how often you manage to ask them; the DMT itself doesn’t cost *that* much per dose (like ~$7) but it’s the all the trips where you don’t get elves or you get elves but are too ecstatic to ask them anything which really kill you and drive up the price to $34-$250 per factoring request. Also, there’s a lot of uncertainty in all these estimates (who knows how much any of the quoted rates differ from person to person?).

I thought this might be a fun self-experiment to do, but looking at the numbers and the cost, it seems pretty discouraging.

Related Empirical Paradigms for Psychedelic Research:

1. LSD and Quantum Measurement (an experiment that was designed, coded up, and conducted to evaluate whether one can experience multiple Everett branches at once while on LSD).
2. How to Secretly Communicate with People on LSD (a method called Psychedelic Cryptography which uses the slower qualia decay factor induced by psychedelics, aka. “tracers”, in order to encode information in gifs that you can only decode if you are sufficiently high on a psychedelic).
3. Psychophysics for Psychedelic Research: Textures (an experimental method developed by Benjamin Bala based on the textural mongrel paradigm proposed by Eero Simoncelli and extended to provide insights into psychedelic visual perception. See: analysis).