[Rafael-SOWNet]

Fixes #2230. Raised by @Happypig375 on #2221.

Primes.IsPrime was trial division, decided only for a number that fits a long. It had three defects:

• It hung. The loop was divisor * divisor <= value. Past divisor = 3037000499 the square overflows long and wraps negative, so for a prime between 3037000499² and 2^63 the loop ran until the divisor reached the number itself.
• It was slow: about 1.5 · 10^9 divisions for a prime near 2^63, and 1.1 s for 2^61 - 1.
• It left every number past 2^63 open: the Mersenne prime 2^89 - 1 and the composite 2^67 - 1 alike.

It is now:

• Miller–Rabin to the first thirteen primes as bases, which is exact below ψ13 = 3317044064679887385961981, the least strong pseudoprime to all thirteen. The bound is from Sorenson and Webster, Strong pseudoprimes to twelve prime bases, Math. Comp. 86 (2017). The first twelve bases already suffice below 2^64.
• Lucas–Lehmer for a Mersenne number 2^p - 1, after checking that p is prime, for p up to 5000.
• Past ψ13, up to 4096 bits, a failed round still proves a number composite. A number that passes every round is left open, since passing is not a proof.

The compiled PP membership from #2223 calls the same test for any whole double; it had been left open past 2^63.

	2.6.0	now
9223372036854775783 in PP	does not finish; stopped after 60 s	True, in 81 ms
(2^89 - 1) in PP	left as written	True
(10^30 + 1) in PP	left as written	False
(10^30 + 57) in PP, a prime past ψ13	left as written	left as written

#2221's MembershipInASetOperationTest and its BREAKING-CHANGES entry used 2^89 - 1 as a number PP leaves open. Lucas–Lehmer now decides it, so both use 10^30 + 57 instead, with [0; 10^31] as an interval that holds it. The entry's values are re-measured on 2.6.0 and on this build.

Tests. PrimalityTest has:

• 16 decided cases under a 30-second cap: the largest prime below 2^63, seven Mersenne numbers from 2^61 - 1 to 2^4423 - 1, the least strong pseudoprime to the first twelve bases, Carmichael numbers and base-2 strong pseudoprimes;
• two cases that stay open;
• every n below 200000, checked against a sieve;
• 2000 random odd n below 10^12, checked against trial division.

Full suite 18080/0, interactive trio, AOT smoke 73/0, all frameworks build.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 91.17647% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.67%. Comparing base (a4b7b74) to head (d947f85).

Files with missing lines	Patch %	Lines
...urces/AngouriMath/Functions/NumberTheory/Primes.cs	90.90%	1 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2232      +/-   ##
==========================================
- Coverage   86.67%   86.67%   -0.01%     
==========================================
  Files         310      310              
  Lines       67691    67717      +26     
  Branches    19634    19644      +10     
==========================================
+ Hits        58670    58691      +21     
- Misses       4905     4910       +5     
  Partials     4116     4116              

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.22% <91.17%> (-0.01%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...ngouriMath/Core/Entity/Omni/Entity.Omni.Classes.cs	87.82% <ø> (ø)
Sources/AngouriMath/Numerics/NumberStatements.cs	93.33% <100.00%> (+3.33%)	⬆️
...urces/AngouriMath/Functions/NumberTheory/Primes.cs	80.95% <90.90%> (+3.26%)	⬆️

... and 6 files with indirect coverage changes

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