Prime Number Race/Examples/3n+1 vs. 3n-1

Example of Prime Number Race

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 $608 \, 981 \, 813 \, 029$.

Historical Note

Carter Bays and Richard H. Hudson discovered this fact on Christmas day $1976$.

It has been suggested that this may have been the only opportunity they had to obtain the appropriate computer time.

Sources

• Apr. 1978: Carter Bays and Richard H. Hudson: Details of the First Region of Integers $x$ with $\pi_{3,2} (x) < \pi_{3,1} (x)$ (Math. Comp. Vol. 32, no. 142: pp. 571 – 576)  www.jstor.org/stable/2006165

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $608,981,813,029$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $608,981,813,029$