What's it called when a prime is made up of perfect squares.

1 is a perfect square

p=1+1...+1

solved

>>8670994
didn't even smirk.. just wondering why you bothered.

>>8670992
Never heard of this particular case. You can probably name them.

But if you are going to name them you better have an important theorem first.

Are there infinitely many primes made up of perfect squares?

well actually 8 isn't a perfect square, so 499 is the first.

but, 89 is the first one made up of non-primes, and 499 is the next one made up of non-primes.

>>8670992
There will be a shitton of them from the form: [1^2 + n^2 = p] ie: 1+1=2, 1+4=5, 1+16=17, 1+36=37, 1+100=101... etc
Also, there will be a lot of them from the form: [n^2 + (n+1)^2 = p] ie: 1+4=5, 4+9=13, 16+25=41, 25+36=61, 49+64=113, 81+100=181, 144+169=313... etc

>>8671104
it's not a sum. just the numbers as they are. anything with only 1's 4's and 9's is a prime made of perfect squares.

anything with only 4's 8's and 9's is a prime made up of only non-primes.

499 and 89 are the first, respectively.

>>8671115
>499 and 89 are the first
11, 19 are the first.

>>8671115
>OP did a shit job explaining what they were talking about in their original post
Who would have guessed?
Also there are more before 499.
19, 41, 149, 191, 419, 449, 491

>>8671123
>>8671140
1 is a prime. 89 is the first.

>>8671141
>1 is a prime

2 is the first prime retard

>>8671141
>What's it called when a prime is made up of perfect squares.
GTFO brainlet who can't read.

>>8670992
These were studied by Ramanujan. In fact, there's a very famous story about them. According to legend, G.H. Hardy came to visit him on his deathbed. Upon arriving in his hospital room, Hardy remarked that the number of the cab he had taken was 89, which he regarded as a completely unremarkable number. Ramanjuan instantly replied: "In fact it is a very interesting number! It is the smallest prime whose digits are expressible as perfect squares in two different ways!".

For this reason, such numbers are often called "Taxicab numbers".

>>8671147
>8
>perfect square
Ramanujan pls

>499 is the first prime number that's made of perfect squares that aren't 1.
this is the brainlet prime.

>89 is the first prime number made of non-primes that aren't 1
this is the /sci/ prime

I tried to write a script to print them but I got a segfault cause I can't into C

>>8670992
>>8670992 (OP)
they are called
https://en.wikipedia.org/wiki/Pythagorean_prime

see also
https://en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares