Definition:Prime Number Race
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Definition
The set of prime numbers $\Bbb P$ may be partitioned into subsets according to a particular property.
A prime number race is a comparison of the count of the number of prime numbers in each partition with increasing $p \in \Bbb P$.
Examples
$4 n + 1$ vs. $4 n - 1$
The sequence of prime numbers at which the prime number race between prime numbers of the form $4 n - 1$ and $4 n + 1$ are tied begins:
- $2, 5, 17, 41, 461, 26 \, 833, 26 \, 849, 26 \, 863, 26 \, 881, 26 \, 893, 26 \, 921, 616 \, 769, \ldots$
$3 n + 1$ vs. $3 n - 1$
In the prime number race between prime numbers of the form $3 n - 1$ and $3 n + 1$, the prime numbers of the form $3 n + 1$ overtake those of the form $3 n - 1$ for the first time at $608 \, 981 \, 813 \, 029$.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $26,861$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $26,861$