If p1 p2 p3 pn are distinct odd prime numbers then p1p2p3pn +1 is always a

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p_{1}^{2} - p_{2}^{2}

n

n = p_{1}^{a_{1}} \cdot p_{2}^{a_{2}} \cdot p_{3}^{a_{3}} . . . . p_{k}^{a_{k}}

p_{1}, p_{2}, p_{3}, . . ., p_{x}

log n > k log 2

If a random variable X assume values x₁, x₂, x₃, …, x_n with the corresponding probabilities p₁, p₂, p₃, …, p_n. Then

N = p_{1} p_{2} p_{3}

p_{1}, p_{2}, p_{3}

\sum d = 3 N o r σ (N) = 3 N

\sum_{i = 1}^{N} \frac{1}{d_{i}} = 3.

a_{1} > a_{2} > a_{3} > . . . . > a_{n} > 1.

p_{1} > p_{2} > p_{3} > . . . . > p_{n} > 0

p_{1} + p_{2} + p_{3} + . . . + p_{n} = 1.

F (x) = (p_{1} a_{1}^{x} + p_{2} a_{2}^{x} + . . . + p_{n} a_{n}^{x})^{1 / x}

lim x \to - \infty F (x)

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