Initial Data Release

Initial draft & dataset upload for primes of the form 2^256 - 2^32 - mx where 0 < c < 2^31.

Decompress 256.sqlite3.xz into the data/ directory, the Python utilities can then be used.

You need: GNU make, sage, gmpy2, pandoc etc. to produce the README.pdf and all graphs.

sqlite> .schema
CREATE TABLE primes_2p256_m2p32_mx (
            mx INTEGER PRIMARY KEY
        );
CREATE TABLE cornacchia_2p256_m2p32_mx (
            mx INTEGER PRIMARY KEY,
            a TEXT NOT NULL,
            b TEXT NOT NULL
        );
CREATE TABLE trial_division_2p256_m2p32_mx (
            mx INTEGER PRIMARY KEY,
            factors_json TEXT NOT NULL,
            remaining_is_prime INTEGER NOT NULL,
            remaining_log2 REAL NOT NULL
        );
CREATE TABLE generator_2p256_m2p32_mx (
            mx INTEGER PRIMARY KEY,
            g INTEGER NOT NULL
        );
CREATE TABLE curves_2p256_m2p32_mx (
            mx INTEGER,
            generator_power INTEGER NOT NULL,
            is_prime INTEGER NOT NULL,
            offset_eisenstein_c INTEGER NOT NULL,
            offset_eisenstein_d INTEGER NOT NULL,
            PRIMARY KEY (mx, generator_power)
        );
CREATE TABLE glv_2p256_m2p32_mx (
            mx INTEGER,
            generator_power INTEGER NOT NULL,
            beta_val TEXT,
            lambda_val TEXT,
            beta_i INTEGER,
            lambda_i INTEGER,
            PRIMARY KEY (mx, generator_power)
        );
CREATE TABLE curvefactor_2p256_m2p32_mx (
            mx INTEGER,
            generator_power INTEGER NOT NULL,
            order_offset INTEGER NOT NULL,
            factors_json TEXT NOT NULL,
            n_factors INTEGER NOT NULL,

            -- Distribution metrics
            entropy REAL NOT NULL,

            -- Size metrics (all log2 values)
            largest_prime_powered_log2 REAL NOT NULL,
            largest_prime_log2 REAL NOT NULL,
            smallest_prime_log2 REAL NOT NULL,
            smallest_prime_powered_log2 REAL NOT NULL,
            second_largest_prime_log2 REAL NOT NULL,

            -- Central tendencies (all log2 values)
            avg_prime_powered_log2 REAL NOT NULL,
            avg_prime_log2 REAL NOT NULL,
            median_prime_powered_log2 REAL NOT NULL,
            median_prime_log2 REAL NOT NULL,

            -- Variance and standard deviation (log2 space)
            var_prime_powers_log2 REAL NOT NULL,
            var_prime_log2 REAL NOT NULL,
            std_prime_powers_log2 REAL NOT NULL,
            std_prime_log2 REAL NOT NULL,

            -- Power distribution (raw integer values)
            max_prime_power INTEGER NOT NULL,
            total_prime_powers INTEGER NOT NULL,

            PRIMARY KEY (mx, generator_power, order_offset)
        );