Q: prime factor 50234
A: ok. it's even, so in half is 25117 (easily seen as 50 2 34 going to 25 1 17). checking for 3, so knock 117, and 25 not, so no 3. checking 7, knock the 7, =2511, knock left from 21, =111, which is known (37x3) so no. checking 11 (in 25117) knock left from 22, = 311, knock 11, =3 (not 11). checking 13 (in 25117), up to 25130, =2513, knock the 13 left with 25=no. checking 17 (in 25117), knock from right, =251, knock 51 (knowkn 17x3), left with 2=no. checking 19 (in 25117), knock back from left = 6117, knock left back again to 57, = 4117, knock back left again to 38, = 317, known prime, but in case you're not sure, knock the left back again so it's 12 7 (127) even more well known prime, or if you don't believe me and feel like subtracting 57 (known 19x3) and knock the zero you must be at a single digit number (no 19) that's without even requiring you to bother subtracting 57 from 127. checking 23 (in 25117), from the right, up to 2514(0), 2514, knock down the left, 214, in half is 107 nope (known prime, the first 100s decade is a known 'full house'). checking 29 (in 25117). known trick: 203. add 203 is 2532(0), in half, is 1250 plus 16, 1266. in half is 633, by 3 is 211. add 29 won't reach 290, so no. checking 31 (in 25117) i'll add 93, = 2521(0). 2521 minus 31, seen as 252-3, = 249 already know that as 83x3 so no (or just add 31, to get 280, =28no.) checking 37 (in 25117), add 333 (the 111 trick x3) is 2544zap i mean 2545. double it, 50 9(0), =509, plus 111 is 620, 62(no) (in half 31no). checking 41 (25117), how about adding 123, = 2532, minus 82 is 245(0), doubled is 39 (3x13) so no. checking 43 (25117) added to right is 2516, in half is 1258, in half is 629, plus 301 (known trick for 43) is 930, no (31x3). checking 47 in 25117, so 2511 minus 4, is 2507, minus 47 means 250 minus 4, is 244, in half is 122, in half 61 so no. checking 53, 25117, = 2517(0), 2517, and 53 added to right again is 257, add to right again is a mildly tedioius 31(0). so no. checking 61 (in 25117). hm, how about 243. knock from left is 817. left can knock back to 20, =207. known 9, so def wrong range for 61. checking 67. 25117 minus 67 is 2505(0). doubled is 501. minus 201 (known trick for 67), =200 so no. checking 71, triple it to 213. 25117 plus 213, = 2513(0), and knock from right is an easy 2300 (=23) so no. checking 73, 25117, add to right is 2519. hm, triple the checker to 219, down to 2300 again, so no. checking 79 (in 25117), ouch, hm, 511 is a trick for 79, ... take that out of the middle? 20007, still not very useful for me unfortunately. must triple 79. that's 240-3 so 237. from 25117, ok, just 2511 minus 23. not fun for me. would be 2477 plus 11, how's that. ok, 2488, half to 1244, to 622, to 311, add 79 to right is 39no. checking 83 in 25117, evens out neatly to 252. half to 126. to 63, (known 7x9) = no. checking 89, i like 801 as a trick here, not the best but decent, triple it is 2403, put that on the right of 25117 is 2 75 20, = 2752. in half, forget it, try doubling the trick (801 to 1602), 2752 minus 1602, = 115. that's 23 so no. checking 97, easy, from right, (25117) is 2502. in half is 1 25 1 (1251), minus 291 (known triple of 97) would be... 10 6. 106, so 53 so no. checking 101, here's where it gets breezy, 25117 plus 303 is 2542(0), in half is 1 27 1 (1271), minus 101 is 117(0), (not 101). checking 103, 25117 add 103 is 2522(0), in half is 1 26 1 (1261), how about plus 309 (103x3). so that's 157(0). not 103 and too close. so no. checking 107. 25117 down to 2501. how about add 321 (triple) so like 250 plus 32. is 282. in half 141. known 47, also clearly no 107. checking 109, let's stop and figure out how high we have to go. 256 has square root of 16. so that means 160 squared is 25600. so if we reach 160 that's far enough. checking 109, or 327. 2511(7), 2511 minus 32, not fun, how about 2468 plus 11. 2479. minus 109 is 237(0), when compared with 327 is clearly wrong for 109. checking 113 (in 25117), add to right is 2523. go down, is 241. in that range it would have had to be 226, so no. checking..127 (that right there is what's known as the 'longest gap so far'), 25117 and down to , wait, 2511 minus 12, is 2499. by 3 is 833. plus 127 puts you evened out at less than 100(0) so no. checking not 129 (that's a 3), check 131. triple it, 393. use 393 on the right, 25117 go up to 2541. down 131 from right, is 241. down 131 goes to 11(0) and out. checking not 133 (that's 19) check 137. 25117, minus 137, means 2511 minus 13, so 2498, in half is 1299, by 3 is 433. is that 137? you would expect 411. (300 plus 111) so no. checking 139, ...... 75351 (just tripled the target number as an escape plan), add 139 to right is 7569, and down to 743. i've been really trying to avoid tripling 139 but i guess i have to, 140 tripled (i'm not good at this) 420, minus 3 is 417. (should have had my 117 more handy as a 39 triple there) 743 plus 417 is 115(0) and that's just 23. (no). checking 141 no that's 47, checking 143 not necessary, checking 147 no that's just 49, checking 149 of course. triple it is 447. 2511(0) minus 44(7).. erm.... 2511 minus 44 i hate my self, is 2464 plus 11 is 2475. double, is 48 no 495(0). double is 99(0) and no. checking 151 (149 and 151 are known twins), triple is 453, 25117 plus 453 means 2512 plus 45, 2557 right? plus 453 should end in 1(0), like 256 plus 45, ok 301. minus 151 definite no, after dropped zero you'd be 2 digits. checking 157, this is the last number to check because 159 would be a 3, and 160 squared is bigger than the target, and if everything so far was done correctly then the only available option left would be 157 squared, which should have to end in 9, which would be wrong, but just in case we'll check 157. 25117, down from right, which would mean 2511 minus 15, so 2496, in half goes to 1248, 624, 312, by 3 is 104 and no. so i am afraid here is where we finally meet the