Numbers of Primes with at most n Digits
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Theorem
Let $p: \Z_{>0} \to \Z_{>0}$ be the mapping defined as:
- $\forall n \in \Z_{>0}: \map p n = $ the number of prime numbers with no more than $n$ digits
Then the value of $p$ for the first few numbers is given below:
$n$ $\map p n$ $1$ $4$ $2$ $25$ $3$ $168$ $4$ $1229$ $5$ $9592$ $6$ $78 \, 498$ $7$ $664 \, 579$ $8$ $5 \, 761 \, 455$ $9$ $50 \, 847 \, 534$ $10$ $455 \, 052 \, 511$
This sequence is A006880 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Historical Note
The number of primes less than $10^{10}$ was calculated by Derrick Norman Lehmer.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $455,052,511$
- 1989: Paulo Ribenboim: The Book of Prime Number Records (2nd ed.)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $168$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $50,847,534$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $455,052,511$