DMT Factoring Experiment Cost Estimate

…“Okay”, I said. “Fine. Let me tell you where I’m coming from. I was reading Scott McGreal’s blog, which has some good articles about so-called DMT entities, and mentions how they seem so real that users of the drug insist they’ve made contact with actual superhuman beings and not just psychedelic hallucinations. You know, the usual Terence McKenna stuff. But in one of them he mentions a paper by Marko Rodriguez called “A Methodology For Studying Various Interpretations of the N,N-dimethyltryptamine-Induced Alternate Reality”, which suggested among other things that you could prove DMT entities were real by taking the drug and then asking the entities you meet to factor large numbers which you were sure you couldn’t factor yourself. So to that end, could you do me a big favor and tell me the factors of 1,522,605,027, 922,533,360, 535,618,378, 132,637,429, 718,068,114, 961,380,688, 657,908,494, 580,122,963, 258,952,897, 654,000,350, 692,006,139?

—“Universal Love, Said the Cactus Person”, by Scott Alexander

[cf. seeing Schrödinger’s cat, psychedelic cryptography, texture perception] I was a little curious about how such an integer factoring experiment would go and how much it would cost.

It looks like one could probably run an experiment with a somewhat OK chance at success for under $1,435.84^$1,000₂₀₁₅.

We need to estimate the costs and probabilities of memorizing a suitable composite number, buying DMT, using DMT and getting the requisite machine-elf experience (far from guaranteed), being able to execute a preplanned action like asking about a prime, and remembering the answer.

1. The smallest RSA number not yet factored is 220 decimal digits. [As of March 2025, RSA-220 through RSA-250 have been factored, and the new smallest unfactored RSA number appears to be RSA-260.]

   The RSA numbers themselves are useless for this experiment because if one did get the right factors, then 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_17ya using ~2,000 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 in 2005_21ya memorized 67k digits of Pi in 1 year! (And Chao says he’s actually memorized 100k, and had intended to recite up to #91,300 but slipped up at #67,891.) So the actual memorization time is not important.

   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 et al 1980, whose digit span went from ~7 to ~80 after 230 hours of training; digit span is much more demanding than a one-off memorization. Kliegl et al 1987 does something similar using more like 80 hours of training. Foer’s Moonwalking With Einstein: The Art & Science of Remembering Everything doesn’t cover much more than a year or two with an undemanding training regimen, and he performed well.

   So I’m going to guesstimate 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. how large are the prime factors? We have to bring back the answer, not just take the question.

   Perhaps a little surprisingly, the sum of the prime factors’ length is going to be about the length of the original composite integer. The Erdős-Kac theorem tells us that that the distribution of the factors is nicely behaved and will be log log n, so even an 800-digit number won’t have an absurd number; and the largest factor will, per the Golomb-Dickman constant, likely be much larger than the second-largest.

   So, the task of memorizing the answer turns out to be fairly similar to memorizing the question. However, the conditions are far more challenging. What if one cannot do so during the DMT trip?

   The relevant mnemonic record might then be “memorizing spoken numbers at a rate of 1 digit⧸second”, where the record ranges from 128 in 2001_25ya to 456 in 2015_11ya. If we dropped back to a smaller number than 800-digits, like a 400-digit challenge, then we could expect the largest prime factor to be ~200 and that would be doable.

   It would not be as good, but it would still be useful as evidence: if you know that a certain 200-digit number is supposed to be a prime factor of your original 400-digit number, then you can first sanity-check that it does divide evenly, and if it does (which will be extremely surprising to you, even if third-parties are unimpressed), you can then cheaply finish factoring the full 400-digit number, as most of the work has been done for you. And then everyone else will be shocked to see the full factorization.

   A challenge here is ensuring that your smaller number is convincing in its own right, if it cannot convince by overwhelming size. You will need some sort of third-party verifiable way to generate the number, like a nothing-up-my-sleeve number.

3. some browsing of the DMT category on the current leading darknet market suggests that 1g of DMT from a reputable seller costs $267.85^₿0.56₂₀₁₅ or ~$186.66^$130₂₀₁₅.

   The linked paper Rodriguez 2006_20ya says smoking DMT for a full trip requires 50mg (0.05g) so our $186.66^$130₂₀₁₅ buys ~19 doses.

4. Rodriguez 2006_20ya 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-elves 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.

5. 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-elves, we might be able to ask 1 time. If the machine-elves are guaranteed to reply correctly, then that’s all we need.

6. at 30 hours of mnemonic labor valued at minimum wage of $11.49^$8₂₀₁₅ and $186.66^$130₂₀₁₅ for 19 doses, that gives us an estimate of $531.26^$370₂₀₁₅ in costs to ask an average of once; if we amortize the memorization costs some more by buying 2g, then we instead spend $358.96^$250₂₀₁₅ per factoring request for 2 tries; and so on down to a minimum cost of (130⁄19) × 5 = $48.82^$34₂₀₁₅ per factoring request.

   To get n = 10 requests, we’d need to spend a cool ((30 × 8) + 10 × 130) = $2,211.19^$1,540₂₀₁₅.

7. 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-elves will not answer or any answer will be ‘forgotten’. (Or you will think you got the answer, but wake up and the response is not a list of prime factors at all but something like “a smell of turpentine prevails throughout”.)

   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 $50.25^$35₂₀₁₅ a shot, you shouldn’t be trying at all). But you probably won’t.

Hence, you could get a few attempts at somewhere under $1,435.84^$1,000₂₀₁₅, 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 ~$10.05^$7₂₀₁₅) 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 $48.82^$34₂₀₁₅–$358.96^$250₂₀₁₅ 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 and the risk of returning with an underwhelming or partial answer, they are discouraging.