Continuing the porting of stuff from betaveros.stash, and adding more stuff.
Mnemonic
Here’s my mnemonic table for digits, inspired by an old Martin Gardner column. I wrote from memory the first 132 digits of 2012! correctly at IMO 2012 with this table. I had remembered more, but unfortunately, if I recall correctly, I confused myself over whether I had encoded a 5 or a 2 by the S of “nose”, because this is supposed to be more of a phonetic code than a spelling one — otherwise double letters would be confusing and lots of randomly appearing digraphs would be wasted, because English is weird.
I assigned two kind of different consonants to 1 because it’s fairly important; I added W pretty late. The other two unused consonants are H and Y.
digit  consonant(s)  mnemonic 

1  L, W  l33t; 1 is pronounced Won 
2  Z(, J, CH, TH)  l33t 
3  M  tilt head sideways 
4  F(, V)  Four 
5  S(, SH)  l33t 
6  G(, K)  l33t 
7  T(, D)  l33t 
8  B(, P)  l33t 
9  N  Nine 
0  R  zeRo, or it’s a Round circle 
Bits & Primes
2095133040 has 1600 factors, the most of any positive integer under 2^{31} − 1. Ref: A002182: highly composite numbers, def. 1
There are 105097565 (1.05e8) primes under 2^{31} − 1.
MillerRabin primality testing does not miss any composites:
 below 2^{31} if the first 3 primes (2, 3, 5) are used as witnesses.
 below 2^{32} if the first 4 primes (2, 3, 5, 7) are used as witnesses.
 below 2^{64} if the first 12 primes (2 to 37 inclusive) are used as witnesses.
See A014233.
To verify implementations: there are 82025 primes beneath (1 << 20)
and 37871 primes between (1 << 40)
and (1 << 40) + (1 << 20)
.
Primes in Decimal

1881881
 n − 1 factorization: 2^{3} × 5 × 7 × 11 × 13 × 47
 smallest primitive root: 6

99990001
 n − 1 factorization: 2^{4} × 3^{2} × 5^{4} × 11 × 101
 smallest primitive root: 13

140000041
 n − 1 factorization: 2^{3} × 3^{2} × 5 × 157 × 2477
 smallest primitive root: 28

987654323
 n − 1 factorization: 2 × 701 × 704461
 smallest primitive root: 2

999299999
 n − 1 factorization: 2 × 23 × 21723913
 smallest primitive root: 11

999992999
 n − 1 factorization: 2 × 499996499
 smallest primitive root: 11

999999001
 n − 1 factorization: 2^{3} × 3^{3} × 5^{3} × 7 × 11 × 13 × 37
 smallest primitive root: 17

999999929
 n − 1 factorization: 2^{3} × 124999991
 smallest primitive root: 3

1000000007
 n − 1 factorization: 2 × 500000003
 smallest primitive root: 5

1000000009
 n − 1 factorization: 2^{3} × 3^{2} × 7 × 109^{2} × 167
 smallest primitive root: 13

1000000021
 n − 1 factorization: 2^{2} × 3 × 5 × 19 × 739 × 1187
 smallest primitive root: 2

1234567891
 n − 1 factorization: 2 × 3^{2} × 5 × 3607 × 3803
 smallest primitive root: 3

2000000011
 n − 1 factorization: 2 × 3 × 5 × 66666667
 smallest primitive root: 2
Primes in Hexadecimal

0xdefaced
 n − 1 factorization: 2^{2} × 3^{2} × 5 × 1298951
 smallest primitive root: 6

0xfacade5
 n − 1 factorization: 2^{2} × 3 × 21914579
 smallest primitive root: 6

0x37beefed
 n − 1 factorization: 2^{2} × 3 × 5 × 1373 × 11353
 smallest primitive root: 6

0x3c0ffee1
 n − 1 factorization: 2^{5} × 7 × 2113 × 2129
 smallest primitive root: 3

0x3de1f1ed
 n − 1 factorization: 2^{2} × 11 × 23595857
 smallest primitive root: 3

0x3efface5
 n − 1 factorization: 2^{2} × 3^{2} × 37 × 47 × 16883
 smallest primitive root: 2

0x5eedbed5
 n − 1 factorization: 2^{2} × 7 × 53 × 199 × 5393
 smallest primitive root: 10
Floating Point
 Singleprecision: sign 1b, exponent 8b, fraction 23+1b implied (= 6 ~ 9 decimal sigfigs)
 Doubleprecision: sign 1b, exponent 11b, fraction 52+1b implied (= 15 ~ 17 decimal sigfigs)
Special cases:
 Exponent = 0
 fraction = 0: (±) zero
 fraction ≠ 0: “subnormal” number with implied bit set to 0 instead
 Exponent = (FF or 3FF, maximum value in allocated bits)
 fraction = 0: (±) infinity
 fraction ≠ 0: NaN (sign ignored)
 top explicit fraction bit = 1: “quiet NaN”
 top explicit fraction bit = 0 (and rest ≠ 0): “signaling NaN”