factordbrpc · fdb
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Enter a value, an expression, or a term with a variable like 10^n+1 to list a range. Switch to Database id to look a number up by its stored id. Reading never stores anything; use Create to add a number to the database. See the expression syntax & functions reference.

P · Proven prime
below threshold 2 digits
★
Interesting number. 1681 = 41^2, the first composite value of Euler's prime-generating polynomial n^2+n+41 (at n = 40), after 40 primes in a row.

Value

41
41
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Term #3 of the Inverse home prime · Base 3 sequence of 4 · 4 terms
Term #1 of the Home prime · Base 12 sequence of 15 · 2 terms
Term #1 of the Home prime · Base 14 sequence of 26 · 2 terms
Term #1 of the Home prime · Base 15 sequence of 22 · 2 terms
Term #1 of the Home prime · Base 17 sequence of 14 · 2 terms
Term #1 of the Home prime · Base 18 sequence of 10 · 2 terms
Term #1 of the Home prime · Base 19 sequence of 6 · 2 terms
Term #1 of the Aliquot variants · Quasi · σ(n) − n − 1 sequence of 30 · 2 terms
Term #1 of the Inverse home prime · Base 13 sequence of 6 · 2 terms
Term #1 of the Conway climb · Base 12 sequence of 15 · 2 terms
Term #1 of the Conway climb · Base 13 sequence of 9 · 2 terms
Term #1 of the Conway climb · Base 14 sequence of 26 · 2 terms
Term #1 of the Conway climb · Base 15 sequence of 22 · 2 terms
Term #1 of the Conway climb · Base 17 sequence of 14 · 2 terms
Term #1 of the Conway climb · Base 18 sequence of 10 · 2 terms
Term #1 of the Conway climb · Base 19 sequence of 6 · 2 terms
Term #1 of the Prime-stopping maps · σ(n) − 1 until a prime sequence of 20 · 2 terms
Term #1 of the Distinct-prime home prime, descending · Base 3 sequence of 26 · 2 terms
Term #1 of the Mid-divisor concatenation · Base 3 sequence of 20 · 2 terms
Is factor of

Primality

Verified directlyproven prime

Checked deterministically (below 300 digits).

From the command linefdb · curl
fdb
fdb number '41' --detail 2
curl
curl -s 'https://factordb.com:4059/rpc' -H 'Content-Type: application/json' -d '{"jsonrpc":"2.0","id":1,"method":"get_number","params":{"target":{"expr":"41"},"decimal":false,"detail":2}}'