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THE 42 INDEX

Sum of three cubes

42

Calculated

x³ + y³ + z³ = 42. Booker and Sutherland, 2019.

The three integers whose cubes sum to 42, with three cubes drawn in line perspective.

(−80538738812075974)³ + 80435758145817515³ + 12602123297335631³ = 42. Booker and Sutherland, PNAS 2021.

ImageBOOKER AND SUTHERLANDComputed

x³ + y³ + z³

(−80 538 738 812 075 974)³+ 80 435 758 145 817 515³+ 12 602 123 297 335 631³

= 42

Three enormous cubes, one of them negative, add up to 42. Last unsolved number below 100. Booker and Sutherland, 2019. They noticed Adams. We did not invent the rhyme.

The last unsolved case below 100. Booker and Sutherland found three cubes in 2019. The researchers noticed Adams. We did not invent that rhyme.

What it supports

A solved Diophantine equation. (−80538738812075974)³ + 80435758145817515³ + 12602123297335631³ = 42. Charity Engine’s volunteer machines ran the search. University of Bristol called it a planetary-scale computer. The Adams association is in the public record of the work.

What it does not

Not a proof that 42 is a physical constant. Not Deep Thought. The joke is reception, documented by the finders, not a second cosmic law.

Calculation

(−80538738812075974)³ + 80435758145817515³ + 12602123297335631³ = 42

Integer search for x³ + y³ + z³ = k, k = 42

ExactnessExact

Form42

Unitinteger

Strengthhard

When2019-09

Source

Booker & Sutherland 2021 · PNAS 118:e2022377118

Owner

THE 42 INDEX