Mathematics
The 3 × 3 × 3 magic cube with rows summing to 42.
- Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3×3×3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, is composed of 3 cubes whose sum of values is 42.
- Forty-two is a pronic number and an abundant number; its prime factorization 2 · 3 · 7 makes it the second sphenic number and also the second of the form { 2 · 3 · r }. As with all sphenic numbers of this form, the aliquot sum is abundant by 12. 42 is also the second sphenic number to be bracketed by twin primes; 30 is also a pronic number and also rests between two primes. 42 has a 14 member aliquot sequence 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 and is itself part of the aliquot sequence commencing with the first sphenic number 30. Further, 42 is the 10th member of the 3-aliquot tree.
- 42 is the product of the first three terms of Sylvester’s sequence; like the first five such numbers it is also a primary pseudoperfect number.
- It is a Catalan number. Consequently; 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc.
- It is the reciprocal of the sixth Bernoulli number.
- It is conjectured to be the scaling factor in the leading order term of the “sixth moment of the Riemann zeta function“. In particular, Conrey & Ghosh have conjectured
- where the infinite product is over all prime numbers, p.[1][2]
- It is the third pentadecagonal number. It is a meandric number and an open meandric number.
- 42 is a Størmer number.
- 42 is a perfect score on the USA Math Olympiad (USAMO)[3] and International Mathematical Olympiad (IMO).[4]
- In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222).
Science
- The atomic number of molybdenum.
- The angle in degrees for which a rainbow appears or the critical angle.
- In 1966, mathematician Paul Cooper theorized that the fastest, most efficient way to travel across continents would be to bore a straight hollow tube directly through the Earth, connecting a set of antipodes, evacuate it (remove the air), and then just fall through.[5] The first half of the journey consists of free-fall acceleration, while the second half consists of an exactly equal deceleration. The time for such a journey works out to be 42 minutes. Remarkably, even if the tube does not pass through the exact center of the Earth, the time for a journey powered entirely by gravity (also known as Gravity train) always works out to be 42 minutes, as long as the tube remains friction-free, as while gravity’s force would be lessened, so would the distance traveled at an equal rate.[6][7] (The same idea was proposed, without calculation by Lewis Carroll in 1893 in Sylvie and Bruno Concluded.[8])
