Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Readable signature
Prime(p)Exact expansion
~(p = 1) /\ forall a b. p = a * b -> a = 1 \/ b = 1This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.
Definition neighborhood
Depends on conservative definitions
none
Used by conservative definitions
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All transitive conservative prerequisites
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Used by theorem statements or local proof propositions
FS000K four_square_odd_prime_half_coordinate_seed FS000L four_square_odd_prime_half_positive FS000M four_square_odd_prime_half_seed_norm_strict FS000N four_square_odd_prime_bounded_modular_seed FS000O four_square_non_two_prime_bounded_modular_seed FS000P four_square_prime_bounded_modular_seed FS000T four_square_branch_odd_represented_strict_step FS000U four_square_bounded_strict_descent_from_odd_signed_quaternion FS001G four_square_descent_strict_multiplier_bounded FS001H four_square_descent_prime_from_strict_step FS001I four_square_descent_prime_from_modular_seed_and_step FS001J four_square_descent_three_mod_four_primes_from_seed_and_step FS001K four_square_lagrange_from_modular_seeds_and_strict_descent FS0021 four_square_descent_nonunit_proper_factor_not_prime FS0023 four_square_descent_bounded_centered_quotient_nonzero FS0024 four_square_descent_odd_centered_strict_step FS0031 four_square_prime_from_strict_descent FS0032 four_square_lagrange_from_strict_descent FS0033 four_square_descent_below_prime_multiplier_bounded FS0034 four_square_prime_from_bounded_strict_descent_and_seed FS0035 four_square_prime_from_bounded_strict_descent FS0036 four_square_lagrange_from_bounded_strict_descent FS003E four_square_prime_two_or_one_mod_four FS003H four_square_prime_case_reduction FS003I four_square_lagrange_bounded_from_primes FS003J four_square_lagrange_from_all_primes FS003K four_square_lagrange_from_three_mod_four_primes FS003L four_square_lagrange_iff_three_mod_four_primes FS003M four_square_prime_from_odd_signed_quaternion FS003O four_square_prime_representation FS0049 four_square_ordered_half_square_injective FS004A four_square_prime_half_square_residues_injective FS004E four_square_half_square_residue_prefix_injective FS004K four_square_odd_prime_modular_seed FS004L four_square_non_two_prime_modular_seed FS004M four_square_prime_modular_seedGrand-campaign planning vocabulary
Locate Prime in the global campaign vocabulary →
Reviewed Prime corresponds to blueprint Prime with checked argument positions [0].
The global atlas describes planning vocabulary and does not itself certify a definition or theorem. The reviewed expansion and conservative dependency DAG on this page are the actual family-local reading definitions.