Thema: Primzahlen aus Differenzen zwischen benachbarten Potenzen bestimmter Differenzen Main table of content: http://www.fermatquotient.com/ Primzahlen: [(B1^N1)^P-(B2^N2)^P]/D oder [(B1^N1)^P+(B2^N2)^P]/D D = B1^N1-B2^N2 oder B1^N1+B2^N2 P ist prim B1, B2, N1, N2 natürliche Zahl > 1 ggT(B1, B2) = 1 ; B1 <> B2 or gcf(B1, B2) = 1 ; B1 <> B2 ggT(N1, N2) = 1 ; N1 <> N2 ; Ausnahme "+" [M] = 2;4;8;16;... entspricht Primzahl der Form [(B1^N1)^M+(B2^N2)^M] oder [(B1^N1)^M+(B2^N2)^M]/2 Siehe auch unter: http://www.primenumbers.net/prptop/prptop.php?page=1#haut --> Search by form --> (x^z-y^z)/w Zusammenstellung der Primzahlen (B1^N1^P-B2^N2^P)/D bzw. (B1^N1^P+B2^N2^P)/D Differenz D (Summe) Potenz (Exponent) P 1 = 3^2-2^3 2 [4] 7 29 31 [32] 67 149 401 2531 19913 30773 53857 170099 2 = 3^3-5^2 [2] 3 [16] 17 61 2777 18211 20183 3 = 2^7-5^3 [2] [4] 619 14767 4 = 5^3-11^2 [16] 23 157 8243 5 = 2^5-3^3 2 [2] 3 13 [64] 71 109 317 409 971 7 = 2^5-5^2 5 [8] 47 53 107 281 439 13033 21001 7 = 2^7-11^2 [4] 61 619 4861 10391 7 = 2^15-181^2 13 233 5449 9 = 253^2-40^3 [2] 107 857 7757 10 = 13^3-3^7 [2] 7 [64] 11 = 3^3-2^4 2 [4] 5 7 13 151 457 691 5009 11 = 56^2-5^5 571 4993 11 = 15^3-58^2 12 = 47^2-13^3 [4] [8] 13 = 3^2+2^2 [2] 3 5 7 11 17 19 41 53 109 167 2207 3623 5059 5471 7949 21211 32993 60251 13 = 2^8-3^5 2 3 631 1291 13 = 17^3-70^2 3 15 = 1138^2-109^3 17 = 3^2+2^3 3 [4] 7 13 19 [32] 307 619 2089 7297 75571 76103 98897 17 = 5^2-2^3 2 [4] [8] 5 31 71 439 6353 17 = 7^2-2^5 3 7 [16] 1021 3221 4241 18397 17 = 23^2-2^9 13 53 1459 17 = 282^2-43^3 7 23 17 = 375^2-52^3 2 5 19 71 3347 17 = 378661^2-5234^3 709 18 = 19^2-7^3 [4] 11 2269 2819 19 = 12^2-5^3 2 3 53 61 167 [1024] 19 = 55^5-22434^2 9511 22 = 7^2-3^3 [4] 409 22 = 47^2-3^7 [4] 5 79 227 23 = 3^3-2^2 2 3 7 61 617 10427 21529 23 = 2^5-3^2 2 [4] 5 31 23 = 2^11-45^2 2 [4] 79 25 = 2^4+3^2 [2] 3 [8] 23 3217 10937 26 = 35^3-207^2 26 = 2537^2-23^5 28 = 37^3-15^4 [2] 17 97 1531 1609 29 = 5^2+2^2 [2] 3 7 19 137 233 30 = 83^2-19^3 31 = 3^3+2^2 5 11 59 173 9839 33 = 5^2+2^3 [4] 5 7 [8] 9439 34 = 5^2+3^2 [2] [4] 11 29 43 61 14107 35 = 11^3-6^4 103 2659 37 = 3788^2-3^15 38 = 37^2-11^3 953 4951 39 = 10^3-31^2 [2] 97 5119 39 = 22^3-103^2 41 = 2^5+3^2 [4] 7 11 13 17 37 41 = 7^2-2^3 3 [4] 5 7 [8] 197 223 233 41 = 13^2-2^7 5 7 [64] 107 317 4513 43 = 3^3+2^4 [4] 7 17 23 101 137 269 7433 44 = 5^3-3^4 [2] 773 44 = 13^2-5^3 [2] [4] 7 17 61 787 1433 8747 46 = 17^2-3^5 [4] 7 10259 11807 47 = 2^7-3^4 [16] 17 61 151 47 = 6^3-13^2 [2] 3 5 7 [64] 761 947 2729 14633 47 = 3^5-14^2 2 9931 47 = 12^3-41^2 47 = 63^3-500^2 [2] [4] 97 49 = 3^4-2^5 2 3 5 [8] 17 1787 2591 49 = 65^3-524^2 81 = 7^2+2^5 11 [16] 61 67 419 2029 3823 81 = 13^3-46^2 100 = 7^3-3^5 3 [4] 19 1627 1861 2381 121 = 5^3-2^2 [2] 3 [4] 61 67 199 643 2237 5657 8933 125 = 11^2+2^2 [2] 3 43 229 419 14827 128 = 71^2-17^3 5 11 71 139 = 3^7-2^11 3 [4] 1249 7109 169 = 12^2+5^2 3 5 [8] 29 169 = 499^2-12^5 43 2027 243 = 7^3-10^2 2 [2] 5 13 31 257 = 15^2+2^5 3 17 31 191 199 7759 257 = 17^2-2^5 [32] 1601 2141 5419 289 = 15^2+2^6 [2] [4] 5 7 1019 343 = 3^5+10^2 [4] 5 23 31 53 67 71 373 4597 7759 8543 12211 Durchsucht bis mindestens N = 10501 [bzw. bis 16384] bzw. bis 33500 Stellen (digits) New 14.09.2019 Update 21.01.2020 Richard Fischer