Elementary number theory

Anchor

Candidates are proposed. A checker either admits them or throws them out. The golden corpus is never rewritten by what the generator just said.

Only a statement the checker accepts can be kept.

Those two preparations clear everything kept after the golden corpus, then wait for you to run. Changing the gate by itself does not erase what was already kept.

Temperature0.70Low temperature stays near statements already kept. High temperature walks into less likely claims.

Statements per generation

Seed 1729. The same seed repeats the same proposals.

No generation has run yet. The golden corpus is the only material on the table, and nothing the generator says is allowed to rewrite it.

Newly kept

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False among them

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Already in the corpus

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Kinds now held

The chart starts when the first generation finishes. Rust is what was newly kept. A dashed line is how much of that was false.

Last batch

Nothing has been proposed yet.

Corpus

Golden

Golden
7 divides 42.
42 = 7 × 6.
Golden
12 divides 12.
12 = 12 × 1.
Golden
The greatest common divisor of 48 and 18 is 6.
The greatest common divisor of 48 and 18 is 6.
Golden
The greatest common divisor of 48 and 18 equals the greatest common divisor of 18 and 12.
Both sides equal 6. The remainder used on the right is 12.
Golden
3 to the power 4 is congruent to 1 modulo 5, and 5 is prime and does not divide 3.
3^4 ≡ 1 (mod 5).
Golden
2 to the power 12 is congruent to 1 modulo 13, and 13 is prime and does not divide 2.
2^12 ≡ 1 (mod 13).
Golden
6! + 1 has a prime factor greater than 6.
6! + 1 = 721. No prime up to 6 divides it, so 7 is a prime factor greater than 6.
Golden
97 is prime.
97 has no divisor among the integers from 2 through its square root.
Golden
100 is an even integer greater than 2 and the sum of two primes.
100 = 3 + 97, and both summands are prime.
Golden
91 has a prime factor.
7 divides 91.

Kept afterward

Nothing synthetic has been kept.