Here Ed's program failed to provide the last 3 fractions before the sp-block. The sp-block itself was derived from the qt-block, after it was identified as such. The positioning of the missing fractions is derived from a property of roots with the qt-block in the middle of the section: corresponding fractions in the first and second half are on opposite sides of the root-value.
Subsequent approximations of √61.
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 23 | 31 | 39 | 86 | 125 | 164 | 289 | 453 | 1070 | 1523 | 4116 | 5639 | 18440 | 24079 | 29718 | 261823 | 291541 | 321259 | 350977 | 380695 | 410413 | 440131 | 469849 | 1379829 | 1849678 | 2319527 | 5108903 | 7428430 | 9747957 | 17176387 | 26924344 | 63596645 | 90520989 | 244638623 | ? | ? | ? | 1766319049 | 13795392780 | ... |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 5 | 11 | 16 | 21 | 37 | 58 | 137 | 195 | 527 | 722 | 2361 | 3083 | 3805 | 33523 | 37328 | 41133 | 44938 | 48743 | 52548 | 56353 | 60158 | 176669 | 236827 | 296985 | 654128 | 951113 | 1248098 | 2199211 | 3447309 | 8142716 | 11590025 | 31322766 | ? | ? | ? | 226153980 | 1766319049 | ... |
| Diophantine equation: | s2-61p2 = 1 | |||
| d = distance to nearest square N2: | -3 | |||
| Smallest non-trivial s: | (2*64-3)/3 | rational: 125/3 | actual: 1766319049 | ⇒ F=3532638098 |
| Smallest non-trivial p: | 2*8/3 | rational: 16/3 | actual: 226153980 | ⇒ primus foldage=226153980 |
| v-value qt-blocks: | 297182-61*38052: | -1 | ||
| Number of series: | 47 |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 1766319049 | ... |
| p | 0 | 226153980 | ... |
| In the numerator: | U(1,1766319049)3532638098 | = | 1/2*U(2,3532638098)3532638098 | - | half the secundus of 3532638098. |
| In the denominator: | U(0,226153980)3532638098 | = | 226153980*U(0,1)3532638098 | - | the 226153980-fold primus of 3532638098. |
| as well as ... | |||||
| In the numerator: | U(0,13795392780)3532638098 | = | 13795392780*U(0,1)3532638098 | - | the 61*226153980-fold primus of 3532638098. |
| In the denominator: | U(1,1766319049)3532638098 | = | 1/2*U(2,3532638098)3532638098 | - | half the secundus of 3532638098. |
| and ... | |||||
| In the numerator: | U(-29718,29718)3532638098 | = | 29718*U(-1,1)3532638098 | - | the 29718-fold quartus of 3532638098. |
| In the denominator: | U(3805,3805)3532638098 | = | 3805*U(1,1)3532638098 | - | the 3805-fold tertius of 3532638098. |