10:04 AM
@Haran Hi. Do you know why Martin Hopf is so rarely on this chat ?
in the last days

1 hour later…
11:15 AM
Define $$f(n):=\sum_{j=1}^n j^{n+1-j}=1+2^{n-1}+3^{n-2}+\cdots +(n-1)^2+n$$
prime for $n=2,34$ , what is the next $n$ for which $f(n)$ is prime ?
perfect power for $n=3$ (only solution ?)

12:00 PM
$f(n)$ upto $n=10^4$ only a perfect power for $n=3$
@TheSimpliFire Hi
I wonder how far Martin Hopf came with the verification of $(n-1)^n+n$ for primality.

2 hours later…
2:26 PM
@NikeDattani ye

2 hours later…
4:09 PM
@Peter Simple answer: I'm working Mo-Fr and math is only one of my hobbys.
Testing the range $(n-1)^n+n$ for $n \le 4 \cdot 10^4$ should be finshed early saturday.

4:37 PM
I just wanted to know which range I can check to help.
@MartinHopf

4:57 PM
$34304^{34305}+34305$ is a hard case LLR couldn't handle. Would be nice if you could check it with PFGW.

5:07 PM
in progress
50000 / 516842
200000

actually I'm testing $34806^{34807}+34807$.

5:36 PM
34304^34305+34305 is composite: RES64: [72F1DB3729D7704B] (873.5990s+0.0005s)
Done.
36224 missing, right ?

5:49 PM
@Peter Thank you Peter.
@Peter I assume LLR to get wrong results only if the base $b$ is of the form $2^k \cdot m$ with $2^k \ge m$.
So the next 'hard case' should occur at base $b=39680$.

36224^36225+36225 is composite: RES64: [998880DD66B111C6] (906.8894s+0.0259s)
Done.
CF 39680 182476 39680^39681+39681<182476> = 1266293051<10> · 6601527111...31<182467>
I have done this already some days ago.
36224 was a "live"-calculation

Well done, so we will complete the search limit soon.

$n^n+3$ has an OEIS-entry, but the search limit was not very high. The issue cases are done until U 205 115954 26240^26240+3<115954> = 4082419812...03<115954>
And the last line was 20240^20240+3 is not prime. RES64: C3A831C9FF97D220. OLD64: 4AF8955DFEC77657 Time : 92.451 sec.
Unfortunately, my new function cannot be handled by LLR
I restart at 20210