List of first emergence of prime gaps p_j..p_(j+1) that show as "negative space" in the Idaho bitmap. Written by Michael De Vlieger, 20210109. The "Idaho" sequence s20210106, defined by David Sycamore. Let a(n) = p_1^e_1 × p_2^e_2 × ... p_ℓ^e_ℓ, where p_1^e_1 = 2^n and ℓ is the maximum possible number of consecutive prime divisors p subject to a condition on the exponents which requires that the exponent ej > 0 is the greatest possible integer for which p_j^e_j < p_(j − 1)^e_(j − 1) for all j ≤ ℓ. We observe that ℓ = ω(a(n)), where ω(n) = A1221(n), the number of distinct prime divisors p | n. This lists the least n for which the adjacent multiplicity difference e_(j+1)-e_j > 1. For convenience we list the "prime gap" to which j pertains, i.e., gap j is that gap between p_j..p_(j+1). The dataset used contains Idaho numbers a(n) for 1 ≤ n ≤ 10000. Herein we do not list j for which n has not yet been found. Prime gap j p(j)..p(j+1) n ---------------------------- 1 2 3 3 2 3 5 7 3 5 7 15 4 7 11 20 5 11 13 59 6 13 17 45 7 17 19 118 8 19 23 80 9 23 29 75 10 29 31 264 11 31 37 119 12 37 41 205 13 41 43 449 14 43 47 262 15 47 53 210 16 53 59 253 17 59 61 758 18 61 67 305 19 67 71 489 20 71 73 1004 21 73 79 384 22 79 83 617 23 83 89 462 24 89 97 400 25 97 101 817 26 101 103 1631 27 103 107 891 28 107 109 1796 29 109 113 974 30 113 127 357 31 127 131 1186 32 131 137 847 33 137 139 2505 34 139 149 609 35 149 151 2811 36 151 157 1042 37 157 163 1096 38 163 167 1652 39 167 173 1191 40 173 179 1248 41 179 181 3621 42 181 191 842 43 191 193 3963 44 193 197 2067 45 197 199 4132 46 199 211 826 47 211 223 896 48 223 227 2540 49 227 229 5006 50 229 233 2619 51 233 239 1858 52 239 241 5367 53 241 251 1246 54 251 257 2020 55 257 263 2091 56 263 269 2175 57 269 271 6307 58 271 277 2256 59 277 281 3378 60 281 283 6680 61 283 293 1511 62 293 307 1223 63 307 311 3865 64 311 313 7619 65 313 317 3969 66 317 331 1356 67 331 337 2925 68 337 347 1907 69 347 349 8833 70 349 353 4587 71 353 359 3186 72 359 367 2536 73 367 373 3338 74 373 379 3421 75 379 383 5109 76 383 389 3551 77 389 397 2762 78 397 401 5432 79 401 409 2885 80 409 419 2445 82 421 431 2560 84 433 439 4163 85 439 443 6172 86 443 449 4294 87 449 457 3324 88 457 461 6507 90 463 467 6651 91 467 479 2492 92 479 487 3663 93 487 491 7130 94 491 499 3770 95 499 503 7350 96 503 509 5057 97 509 521 2752 99 523 541 2021 100 541 547 5572 101 547 557 3538 102 557 563 5767 103 563 569 5851 105 571 577 5966 106 577 587 3809 107 587 593 6136 108 593 599 6236 110 601 607 6370 111 607 613 6445 112 613 617 9532 114 619 631 3540 115 631 641 4280 118 647 653 7058 119 653 659 7141 121 661 673 3879 123 677 683 7461 124 683 691 5721 125 691 701 4763 126 701 709 5941 127 709 719 4923 128 719 727 6106 129 727 733 8163 130 733 739 8268 132 743 751 6401 133 751 757 8494 135 761 769 6580 137 773 787 4107 138 787 797 5611 139 797 809 4857 141 811 821 5836 145 829 839 6012 146 839 853 4519 150 863 877 4708 154 887 907 3649 156 911 919 8364 157 919 929 6889 158 929 937 8562 162 953 967 5313 166 983 991 9127 168 997 1009 6464 172 1021 1031 7863 175 1039 1049 8039 177 1051 1061 8155 180 1069 1087 4982 189 1129 1151 4537 191 1153 1163 9106 193 1171 1181 9263 197 1201 1213 8177 203 1237 1249 8459 205 1259 1277 6076 214 1307 1319 9051 217 1327 1361 4080 221 1381 1399 6876 223 1409 1423 8697 259 1637 1657 7795 263 1669 1693 6941 274 1759 1777 9233 297 1951 1973 8857 327 2179 2203 9448