A team led by Andrew Sutherland of MIT and Andrew Booker of Bristol University has solved the final piece of a famous 65-year old math puzzle with an answer for the most elusive number of all: 42. The number 42 also turns up in a whole string of curious coincidences whose significance is probably not worth the effort to figure out. For example: According to a March 6 Economist blog post marking the 42nd anniversary of the radio program The Hitchhiker’s Guide to the Galaxy, which preceded the novel, “ the 42nd anniversary of anything is rarely observed.” A Purely Arbitrary Choice

All this is amusing, but it would be wrong to say that 42 is really anything special mathematically. The numbers 41 and 43, for example, are also elements of many sequences. You can explore the properties of various numbers on Wikipedia. Deep Thought takes 7.5 million years to calculate the answer to the ultimate question. The characters tasked with getting that answer are disappointed because it is not very useful. Yet, as the computer points out, the question itself was vaguely formulated. To find the correct statement of the query whose answer is 42, the computer will have to build a new version of itself. That, too, will take time. The new version of the computer is Earth. To find out what happens next, you’ll have to read Adams’s books. The answer came in a 2020 preprint, the result of a huge computational effort coordinated by Booker and Andrew Sutherland of the Massachusetts Institute of Technology. Computers participating in the Charity Engine network of personal computers, calculating for the equivalent of more than one million hours, showed: Sutherland, whose specialty includes massively parallel computations, broke the record in 2017 for the largest Compute Engine cluster, with 580,000 cores on Preemptible Virtual Machines, the largest known high-performance computing cluster to run in the public cloud.When I heard the news, it was definitely a fist-pump moment,” says Sutherland. “With these large-scale computations you pour a lot of time and energy into optimizing the implementation, tweaking the parameters, and then testing and retesting the code over weeks and months, never really knowing if all the effort is going to pay off, so it is extremely satisfying when it does.” You cannot get a sum of 4 or 5 (= –4). This restriction means that sums of three cubes are never numbers of the form 9 m + 4 or 9 m + 5. We thus say that n = 9 m + 4 and n = 9 m + 5 are prohibited values. Searching for Solutions For practical purposes we can round our final result to an approximate numerical value. We can say that forty-two centimeters is approximately sixteen point five three five inches:

The factor 2.54 is the result from the division 1 / 0.393701 (centimeter definition). Therefore, another way would be: The number 42 is the sum of the first two nonzero integer powers of six—that is, 6 1 + 6 2 = 42. The sequence b( n), which is the sum of the powers of six, corresponds to entry A105281 in OEIS. It is defined by the formulas b(0) = 0, b( n) = 6 b( n– 1) + 6. The density of these numbers also tends toward zero at infinity. The Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.”This is another reason I really liked running this computation on Charity Engine — we actually did use a planetary-scale computer to settle a longstanding open question whose answer is 42.” That calculation is not the only other solution. In 1936 German mathematician Kurt Mahler proposed an infinite number of them. For any integer p: