Meertens number

In mathematical logic, a Meertens number is an integer that is its own Gödel number.

The Gödel encoding of a decimal number with n digits is the product of the first n primes raised to the values of their corresponding digits in the sequence.

The only Meertens number that has been found is 81312000 = 2⁸3¹5³7¹11²13⁰17⁰19⁰.

It was "given" to Lambert Meertens by Richard S. Bird as a present during the celebration of his 25 years at the CWI, Amsterdam. ^[1]

If other Meertens numbers exist, they must be greater than 1 × 10²⁵.^[2]

References

↑ Richard S. Bird (1998). "Meertens number". Journal of Functional Programming. 8 (1): 83–88. doi:10.1017/S0956796897002931.
↑ Nicolas PALAU : No new Meertens number < 1 × 10²⁵

External links

OEIS sequence A189398 (a(n) = 2^d(1) * 3^d(2) * ... * prime(k)^d(k))

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[1] Richard S. Bird (1998). "Meertens number". Journal of Functional Programming. 8 (1): 83–88. doi:10.1017/S0956796897002931.

[2] Nicolas PALAU : No new Meertens number < 1 × 10²⁵