A construction of 423 distinct primes using exactly 150 copies of each digit 0-9

Counts by length: {1: 4, 2: 21, 3: 138, 4: 260}
Digit usage: {0: 150, 1: 150, 2: 150, 3: 150, 4: 150, 5: 150, 6: 150, 7: 150, 8: 150, 9: 150}
Total primes: 423
Total digit tiles used: 1500
Omitted 3-digit primes: [113, 131, 179, 311, 337]

1-digit primes (4):
2, 3, 5, 7

2-digit primes (21):
11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67
71, 73, 79, 83, 89, 97

3-digit primes (138):
101, 103, 107, 109, 127, 137, 139, 149, 151, 157, 163, 167, 173, 181, 191
193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271
277, 281, 283, 293, 307, 313, 317, 331, 347, 349, 353, 359, 367, 373, 379
383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463
467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571
577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659
661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761
769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863
877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977
983, 991, 997

4-digit primes (260):
1009, 1049, 1063, 1069, 1409, 1609, 1801, 2003, 2027, 2029, 2053, 2063, 2069, 2081, 2083
2087, 2089, 2099, 2203, 2207, 2243, 2251, 2267, 2281, 2287, 2423, 2447, 2459, 2467, 2503
2521, 2543, 2549, 2551, 2609, 2647, 2657, 2659, 2683, 2687, 2689, 2707, 2801, 2803, 2843
2851, 2857, 2887, 2909, 3001, 3041, 3061, 3083, 3089, 3203, 3407, 3803, 4001, 4003, 4007
4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4091, 4099, 4201, 4229, 4241, 4243, 4253
4259, 4261, 4283, 4289, 4409, 4421, 4423, 4441, 4447, 4463, 4481, 4483, 4507, 4523, 4549
4561, 4567, 4583, 4603, 4621, 4643, 4649, 4651, 4657, 4663, 4703, 4801, 4861, 4889, 4909
5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5101, 5209, 5227, 5261
5281, 5303, 5309, 5407, 5443, 5449, 5483, 5501, 5503, 5507, 5521, 5527, 5557, 5563, 5569
5581, 5623, 5641, 5647, 5653, 5659, 5683, 5689, 5801, 5807, 5821, 5827, 5843, 5849, 5851
5857, 5861, 5867, 5869, 5903, 6007, 6029, 6043, 6047, 6053, 6067, 6089, 6091, 6203, 6221
6229, 6247, 6257, 6269, 6287, 6301, 6353, 6421, 6427, 6449, 6451, 6469, 6481, 6521, 6529
6547, 6551, 6553, 6563, 6581, 6607, 6653, 6659, 6661, 6689, 6803, 6823, 6827, 6829, 6841
6857, 6869, 6883, 6907, 7001, 7027, 7043, 7057, 7069, 7207, 7507, 7607, 8009, 8011, 8039
8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8209, 8221, 8243, 8263, 8269, 8287, 8423
8429, 8443, 8447, 8461, 8467, 8501, 8521, 8527, 8543, 8563, 8581, 8609, 8623, 8627, 8629
8641, 8647, 8669, 8689, 8803, 8807, 8821, 8849, 8863, 8867, 8887, 9001, 9007, 9029, 9041
9049, 9067, 9209, 9601, 9803