8192

8192 is the natural number following 8191 and preceding 8193.

8192 is a power of two: $2^{13}$ (2 to the 13th power).

Because it is two times a sixth power (8192 = 2 × 4⁶), it is also a Bhaskara twin. That is, 8192 has the property that twice its square is a cube and twice its cube is a square.^[1]

In computing

8192 (2¹³) is the maximum number of fragments for IPv4 datagram

References

^ Sloane, N. J. A. (ed.). "Sequence A106318 (Bhaskara twins: n such that 2*n^2=X^3 and 2*n^3=Y^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..

[1] Sloane, N. J. A. (ed.). "Sequence A106318 (Bhaskara twins: n such that 2*n^2=X^3 and 2*n^3=Y^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..

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