[Rafael-SOWNet]

Closes #2341. Closes #2342.

	2.6.0 and master	now
MathS.NumberTheory.Factorize(2^64)	OverflowException	(2, 64)
"phi(7^30)".Simplify()	OverflowException	19319434534879078361025642, 41 ms
(2^89 - 1).IsPrime	OverflowException	true
Factorize(9223372036854775783), the largest prime below 2^63	does not finish	itself, 10 ms
phi(2^62)	right, 2.1 s	right, 0.11 s (cold)
Factorize(1000000007 * 1000000009)	right, 1.3 s	right, 74 ms

• TryFactorize: trial division in EInteger up to 65536, bounded by what is left to factor rather than by the running totient. Then Primes.IsPrime (Primality is decided by Miller-Rabin and Lucas-Lehmer, and finishes #2232's Miller–Rabin and Lucas–Lehmer) is asked of the rest, and Pollard's rho splits a rest that is composite. A rest above 65536² with no factor below it is prime once proven so, or its two pieces are each past 65536.
• phi, CountDivisors and Factorize are built on it. Where a factor is neither proven prime nor split (an undecided probable prime past ψ13, or a composite rho does not split within its budget), the public methods throw NotSufficientlySupportedException. phi(n) in an expression is left as written instead of throwing out of Simplify, as the issue asks.
• Integer.IsPrime is Primes.IsPrime, as PP membership is. That is bool? internally. The public bool throws where primality is not decided, rather than becoming bool?, which would break the API. The two phi(p ^ k) rules (the matched one and the pattern) fire only where primality is proven.
• The compiled totient over double, long and int had the same wrapping loop and now takes the same path. The long overload of Phi is gone; it had no caller left.

Tests: AFactorisationPastTheLongsTest, 24 cases, each expected value checked with sympy. 12 fail on master (four by the 30 s cap); the 12 small cases pass on both. The full suite, AOT and the nine harnesses pass. There is a BREAKING-CHANGES entry, measured on 2.6.0.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 74.66667% with 19 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.75%. Comparing base (0731fc1) to head (4422073).
⚠️ Report is 2 commits behind head on master.

Files with missing lines	Patch %	Lines
...rces/AngouriMath/Functions/InternalAMExtensions.cs	74.19%	6 Missing and 10 partials ⚠️
...Continuous/Entity.Continuous.Integer.Definition.cs	50.00%	0 Missing and 1 partial ⚠️
...Math/Core/Transformations/Matching/MatchedRules.cs	0.00%	0 Missing and 1 partial ⚠️
...Evaluation.Discrete/Evaluation.Discrete.Classes.cs	66.66%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2352      +/-   ##
==========================================
- Coverage   86.78%   86.75%   -0.04%     
==========================================
  Files         312      312              
  Lines       68675    68760      +85     
  Branches    19988    20025      +37     
==========================================
+ Hits        59602    59655      +53     
- Misses       4905     4921      +16     
- Partials     4168     4184      +16     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.30% <74.66%> (-0.04%)	⬇️
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
...nctions/Algebra/Polynomials/PolynomialFactoring.cs	98.31% <100.00%> (ø)
...h/Functions/Compilation/IntoLinq/MathAllMethods.cs	74.74% <100.00%> (ø)
...s/Simplification/Patterns/Patterns.NumberTheory.cs	100.00% <100.00%> (ø)
Sources/AngouriMath/Numerics/SpecialFunctions.cs	80.97% <100.00%> (+0.08%)	⬆️
...Continuous/Entity.Continuous.Integer.Definition.cs	80.39% <50.00%> (-1.61%)	⬇️
...Math/Core/Transformations/Matching/MatchedRules.cs	99.55% <0.00%> (-0.03%)	⬇️
...Evaluation.Discrete/Evaluation.Discrete.Classes.cs	89.59% <66.66%> (-0.21%)	⬇️
...rces/AngouriMath/Functions/InternalAMExtensions.cs	83.69% <74.19%> (-1.92%)	⬇️

... and 9 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[Happypig375]

These should definitely be queued for v3 (all API insufficiencies like these need to be queued for v3)

[Rafael-SOWNet]

Queued in #1019, item 18. Integer.IsPrime becomes bool?, null where Miller–Rabin and Lucas–Lehmer leave it open. Factorize, CountDivisors and Phi return null where a factor is neither proven prime nor split, which is #1569's rule. Until v3, this PR throws NotSufficientlySupportedException in those places, so the bool stays as it is.

🤖 Generated with Claude Code