3

3, Prime Number, Deficient Number, Fibonacci Number

3 = 123 − 45 − 6 − 78 + 9

3 = 98 − 76 − 5 + 4 + 3 − 21

3 = 0^5 − 1^9 − 2^7 − 3^8 + 4^6 + 5^3 + 6^1 + 7^4 + 8^2 + 9^0

\( {\displaystyle 3=1^{3}+1^{3}+1^{3}=4^{3}+4^{3}+(-5)^{3} } \)

3 is the sum of 3 positive cubes in exactly 1 way.

\( {\displaystyle 3=569\ 936\ 821\ 221\ 962\ 380\ 720^{3}+(-569\ 936\ 821\ 113\ 563\ 493\ 509)^{3}+(-472\ 715\ 493\ 453\ 327\ 032)^{3}.} \)

2³ - 1 = 7, Mersenne number: 2^p - 1, p Prime

Number k such that (7*10^k + 71)/3 is prime

Number k such that 8*10^k - 49 is prime. (7951)

Number k such that k! - 1 is prime.

3 = 1 + 1 + 1
= 2 + 2/2
= 3
= 4 − 4/4
= 5 − (5 + 5)/5
= 6 × 6/(6 + 6)
= (7 + 7 + 7)/7
= 88/8 − 8
= (9 + 9 + 9)/9

For every integer n, n^3 - n is divisible by 3

Wagstaff number: number k such that (2^k + 1)/3 is prime.

Number k such that the Woodall number kx2^k - 1

integer partitions of 3 (3, 2+1, 1+1+1)

Number of arrangements of 2 circles in the affine plane.

Sophie Germain prime p: 2p+1 is also prime (7)

Number of prime knots with 6 crossings.

Heegner number d, (the ring of algebraic integers of \( \mathbb {Q} \left[{\sqrt {-d}}\right] \) has unique factorization)

Number n which is the sum of 3 nonzero 4th powers:

Numbers k such that 2^k + 9 is prime. (17)

Numbers k such that (8*10^k + 49)/3 is prime.

Number k such that (16*10^k - 31)/3 is prime.

Number k such that (11*10^k + 19)/3 is prime

Number k such that k!! - 1 is prime.

Fermat prime: primes of the form 2^(2^k) + 1, k = 0

Numbers of edges of regular polygon constructible with unmarked straightedge and compass.

2 <--- ---> 4