### Are the rightmost digits of G random?

 Some statistics computed using Fourmilab's ENT test program Rightmost 10000 decimal digits:     entropy: 3.3216 bits per digit (cf. 3.3219... = log2(10) for an infinite random sequence)      chi-square p-value*: 0.8285 (cf. ≥ 0.01 if not significantly different from random)     serial correlation coefficient:  -0.004062 (cf. 0 for an infinite random sequence)     relative digit-frequencies: [0.1032, 0.1007, 0.0972, 0.1014, 0.0979, 0.1016, 0.0999, 0.09970, 0.1025, 0.0959] (cf. all 1/10 for an infinite random sequence)      * This chi-square result was computed with custom software, since ENT assumes sampling from 256 byte-values (instead of only ten).  Rightmost 10000 decimal digits converted to binary (33216 bits):     entropy: 0.99994 bits per bit (cf. 1 for an infinite random sequence)      chi-square p-value: 0.0975 (cf. ≥ 0.01 if not significantly different from random)      serial correlation coefficient: -0.004057 (cf. 0 for an infinite random sequence)     relative digit-frequencies: [0.5045, 0.4955] (cf. both 1/2 for an infinite random sequence) Some statistics computed using the NIST Statistical Test Suite  Rightmost 20000 binary digits of G: ``` Test Result (p-values) Block length --------------------------------- ------------------------- -------------- Frequency (Monobit) PASS (0.213313) Frequency Test within a Block PASS (0.631448) M=200 Runs PASS (0.504183) Longest-Run-of-Ones in a Block PASS (0.593697) M=128 (preset) Non-overlapping Template Matching PASS* 146 of 148 patterns m=10 Serial PASS (0.593483, 0.619471) m=10 Approximate Entropy PASS (0.488289) m=9 Cumulative Sums PASS (0.349060, 0.107114) PASS means the p-value is at least 0.01 *cf. the rightmost 20000 bits of pi PASS 147 of the 148 patterns in this test. ``` Tentative conclusion     Treated simply as test data, these digit strings do not exhibit significant departures from randomness (as far as these few tests are concerned).