Do gaps between consecutive odd primes form a Gaussian distribution that becomes flat for the entire natural number line?
Plot gap size (x-axis) versus number of gaps (y-axis) with that gap size.
Here's an example.
Between primes, 1 and 349, we generate and plot the set,
S_1 = {(x, y) | (2, 22), (4, 16), (6, 20), (8, 1), (10, 5), (12, 2), (14, 3)};
Between primes, 1 and 809, we generate and plot the set,
S_2 = {(x, y) | …};
Between primes, 1 and 1,811, we generate and plot the set,
S_3 = {(x, y) | …};
Between primes, 1 and 4,057, we generate and plot the set,
S_4 = {(x, y) | …};
Between primes, 1 and 9,011, we generate and plot the set,
S_5 = {(x, y) | …};
Between primes, 1 and 19,793, we generate and plot the set,
S_6 = {(x, y) | …};
Between primes, 1 and 42,841, we generate and plot the set,
S_7 = {(x, y) | …};
Between primes, 1 and 92,753, we generate and plot the set,
S_8 = {(x, y) | (2, 1146), (4, 1143), (6, 1826), (8, 723), (10, 850), (12, 911), (14, 461), (16, 318), (18, 477), (20, 217), (22, 206), (24, 179), (26, 76), (28, 89), (30, 139), (32, 28), (34, 31), (36, 45), (38, 18), (40, 26), (42, 17), (44, 5), (46, 2), (48, 3), (50, 4), (52, 7), (54, 4), (56, 1), (58, 4), (60, 1), (62, 1), (64, 1), (72, 1)};
Between primes, 1 and 199,207, we generate and plot the set,
S_9 = {(x, y) | (2, 2154), (4, 2128), (6, 3446), (8, 1385), (10, 1700), (12, 1816), (14, 957), (16, 632), (18, 1032), (20, 467), (22, 440), (24, 454), (26, 197), (28, 216), (30, 319), (32, 67), (34, 90), (36, 115), (38, 57), (40, 66), (42, 57), (44, 14), (46, 20), (48, 18), (50, 11), (52, 11), (54, 18), (56, 4), (58, 7), (60, 10), (62, 2), (64, 2),(66, 1), (68, 1), (70, 3), (72, 1), (78, 1), (86, 1)};
Between primes, 1 and 425,849, we generate and plot the set,
S_10 = {(x, y) | (2, 4012), (4, 3999), (6, 6529), (8, 2656), (10, 3310), (12, 3689), (14, 1948), (16, ****), (18, 2141), (20, 1022), (22, 917), (24, 1072), (26, 451), (28, ***), (30, 726), (32, 204), (34, 219), (36, 274), (38, 135), (40, 165), (42, 165), (44, 57), (46, 54), (48, 56), (50, 34), (52, 25), (54, 51), (56, 12), (58, 19), (60, 31), (62, 6), (64, 6),(66, 14), (68, 4), (70, 8), (72, 2), (74, 1), (76, 2), (78, 3), (82, 1), (86, 2), (90, 1), (96, 1), (100, 1), (112, 1)};
…
This project is ongoing.
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