2

two

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m | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 2 mod m | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2

2 has a representation as a sum of 2 squares: 2 = 1^2 + 1^2

2 is the 3rd Fibonacci number (F_3).

2 = 2!

2 is the number of derangements of 3 objects.

2 is the 2nd Catalan number (Catalan(2)).

2 is the 2nd Bell number (B_2).

2 is the 2nd Motzkin number.

2 is a Sophie Germain prime, since 2 2 + 1 = 5 is also prime.

2 is the number of integer partitions of 2 (p(2)).

2 is the number of integer partitions of 4 into distinct parts (q(4)).

2 is the 1st prime number.

2 is an even number.

2 is the exponent of the Mersenne prime 3 = 2^2 - 1.

e^(π sqrt(2))≈85.0197 is a near-integer, and the ring of integers of the associated field Q(sqrt(-8)) has unique factorization.

0, 1

1

0.5

p_2 = 3 | p_3 = 5

p_1 = 1 + sum_(k=1)^(2^1) floor(1/(1 + π(k)))

p_1 = 2 + sum_(k=2)^floor(2 + 2 log(1))(1 - floor(π(k)))

p_1 = sum_(k=0)^1 g(1 - g(-1 + sum_(j=0)^k r((g(-1 + j)!)^2, j))) for (g(m) = m θ(m) and δ_(0, b) (a - a mod b) + a mod b = r(a, b))