The world was recently stunned by the news that the supercomputers used to power the Bitcoin trading system employ as much power each year as the whole of Argentina. The story came to light because experts have been perplexed as to why the crypto-currency’s energy requirement is increasing far more quickly than are the actual number of transactions.
These require the heavy use of prime numbers – integers such as 2, 3, 5 and 7 that are only exactly divisible by themselves and one. The reason for the surge in the power needs has now been revealed: the prime numbers are being so over-used that many of them are no longer fit for purpose.
“Evidence suggests that numbers behave differently in these intense conditions,” explained Professor Donald Croclack of University College, Cambridge. “At sub-atomic levels, the laws of Newtonian physics no longer apply. It appears the same thing is happening to prime numbers when exposed to the massive pressures demanded by Bitcoin calculations.”
Research so far has concentrated on the number seven. In some intense situations it now behaves as if it is exactly divisible – though by what, no one is yet sure. At present, this has only been detected in very high-end calculations but the fear is that this tendency will increase and perhaps spread to other numbers. The reasons for this have yet to be fully understood.
“Think of helium,” Professor Croclack disconcertingly suggested. “It’s inert and forms no compounds and so can be seen as one of chemistry’s prime numbers. However, in the high pressures and temperatures found in stars it can break down, combine and change its behaviour. Something of that kind seems to happening with prime numbers.”
They’re mutating, in other words? we suggested. “I didn’t say that,” Professor Croclack replied.
Whether a mutation or not, this discovery leaves Bitcoin’s crypto-boffins with a dilemma. Either their global operations are scaled back, which it’s hoped will lead to the primes returning to their previously inert state; or they continue, with the result that more new primes need to be mined to feed the insatiable demands of the online speculators.
There are two problems with the latter approach. The first is that, the longer the prime number – and the systems already routinely use one several hundred digits long – the more processing will be required, so increasing the problem. The other is the uncertainty of whether it’s only seven in isolation, or any prime number containing seven, that is affected. “That’s a big question,” Professor Croclack admitted. “So far, it seems that longer numbers behave normally. However, we’ve got a close eye on 11 and 13. If they start to blow, we’re into a world of pain.”
What form might this pain take? Crypto-codes would be an immediate casualty, which would prevent almost any online transaction. The still greater fear is that this change might, like a virus, “jump species” to the numbers that we use on our spreadsheets or cash tills. “If seven can acquire an evolutionary advantage from not being a prime number then it will do so,” Professor Croclack admitted. He added that the government had run a simulation exercise, Operation Oliver, about the possibility of prime-number collapse in 2016 but that “the results were not published as the implications were too alarming.” It’s understood that no government action has since been taken into preparing for this threat. Plans for multi-million pound facility in Oxford to looking creating artificial prime numbers was quietly dropped in 2018 while in the same year the then Prime Minister Theresa May vetoed the creation of a “Prime Number Tsar” to oversee the official response to the threat.
Very recent information revealed to Opening Gambit suggests that the nightmare scenario may now be upon us. Research from the Chalfont-Camden Institute in Sydney, which has been looking at the same issue, suggests that, at similar high-pressure conditions, the number four not only regards itself as prime but also as being odd. Worse still, this feature was also reported as having appeared on the laptop calculator of one of the researchers, leading to the fear that the mutation had indeed jumped through human transmission. We put this news to Professor Croclack: even through the imperfect medium of Zoom, it was easy to tell that he had become ashen-faced.
“This hasn’t been peer-reviewed yet,” he finally said. We pressed him further: what if it were true? “Well,” he said, “if so, it’s a complete game changer. Prime numbers that think they’re divisible, even numbers that think they’re odd – this undermines the whole fabric of our world. If so, forget climate change as a threat. As a species, this will finish us off in three months. Or four…” At that point, the connection was broken.
First seen on Penny Post