Exercise 3.6.3 (Maximum value of $r(n)$ for positive $n \leq 10000$)

Question

What is the maximum value of $r(n)$ for positive $n \leq 10000$?

Richard Ganaye · Accepted Answer

\begin{proof} Note that $r(1105) = r( 5 \cdot 13 \cdot 17) = 2^{2+3} = 32$. If we want to improve this score, we must introduce a fourth prime of the form $4k+1$, the least of them being $29$. But $5 \cdot 13 \cdot 17 \cdot 29 = 32045 >10000$, thus the maximum value of $r(n)$ for positive $n \leq 10000$ is $32$.
\end{proof}

Check (with the function $r(n)$ given in Problem 1):

\begin{verbatim}
nrec, maxi = 0, 0
for n in range(1,10001):
    rec = r(n)
    if rec > maxi:
        nrec = n
        maxi = rec
print(nrec, maxi)

(1105, 32)
\end{verbatim}

Exercise 3.6.3 (Maximum value of $r(n)$ for positive $n \leq 10000$)

Answers

Comments

Exercise 3.6.3 (Maximum value of $r(n)$ for positive $n \leq 10000$)

Answers

Comments

Add answer