# RFC 3526 - What does pi mean?

In RFC 3526 there are a series of primes listed as standard parameters used for Diffie-Helman. The primes are list in two formats. One is the long format, where the number is given in hex. For example:

  FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
670C354E 4ABC9804 F1746C08 CA237327 FFFFFFFF FFFFFFFF


Then they have the short hand version:

$$2^{1536} - 2^{1472} - 1 + 2^{64} * ( [2^{1406} pi] + 741804 )$$

Obviously, the short version takes less space in code. The question is: how do I interpret it? What is the meaning of the $pi$ term in the square brackets?

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Surely that means integer part of pi * 2^1406? –  figlesquidge Feb 12 at 21:57

$\pi$ is the transcendental number 3.1415926...

It's there in the formula to show this specific number was not chosen with a specific cryptographical backdoor in mind; it seems unlikely that anyone was able to select the value of $\pi$ (unless Carl Sagan was correct, of course :-)

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I assumed it had some special meaning in this context but you're telling me it's just a "nothing up my sleeve number?" Man, I feel dumb now. –  Simon Johnson Feb 12 at 22:05
@SimonJohnson: Yes; it's there not because we expect it to have some special property, but instead because we don't. –  poncho Feb 12 at 22:07