XPost: sci.math.num-analysis
From: nospam@needed.invalid
On Fri, 2/20/2026 3:16 AM, David Brown wrote:
> On 19/02/2026 23:39, Keith Thompson wrote:
>> David Brown writes:
>> [...]
>>> As a deterministic function, a PRNG will obviously follow the pattern
>>> of its generating function. But the aim is to have no /discernible/
>>> pattern. The sequence 3, 4, 2, 1, 1, 7, 0, 6, 7 has no pattern that
>>> could be identified without knowledge of where they came from - and
>>> thus no way to predict the next number, 9, in the sequence. But there
>>> is a pattern there - it's the 90th - 100th digits of the decimal
>>> expansion of pi.
>> [...]
>>
>> A Google search for 342117067 gives numerous hits referring to the
>> digits of pi.
>>
>
> That is using knowledge of where the sequence comes from - something else's
knowledge rather than your own, but it's the same principle.
>
"In the following sequence, what is the next digit 7,7,7,7,7,7,7,7,7 ? " :-)
PI=3.
1415926535 8979323846 2643383279 5028841971 6939937510
...
7777777772 4846769425 9310468643 5260899021 0266057232 # Line 517834
I suspect seeing that, that's not good.
Using pgmp-chudnovsky.c , and dumping pi as a binary float to a file,
I get this:
(text version of PI) 100,000,022 bytes
PI-Binary.bin 41,524,121 bytes exponent and limbs
PI-Binary.bin.7Z 41,526,823 bytes 7Z Ultra compression, running on
1 core
The entropy property looks pretty good, but I doubt I would
be using that for my supply of random numbers :-)
https://gmplib.org/list-archives/gmp-discuss/2008-November/003444.html
https://stackoverflow.com/questions/3318979/how-to-serialize-the-gmp-mpf-type
https://gmplib.org/list-archives/gmp-discuss/2007-November/002981.html
gcc -DNO_FACTOR -fopenmp -Wall -O2 -o pgmp-chudnovsky pgmp-chudnovsky.c -lgmp
-lm
Paul
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