WON TOPIC 171

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[ May 21, 2007 ]
A random walk around the powers of ten
A conjecture of Milton L. Brown (email)

Source material for borderprimes around powers of ten.

Let 10ⁿ+x be the smallest PRP (prime) past 10ⁿ
let 10ⁿ–y be the largest PRP (prime) before 10ⁿ

Then f(n) = x–y and F(n) = sum f(m) for m = 1 to n

F(n) is negative for values of n in the first set of brackets,
and positive for values of n in the second set of brackets below.

F(n) remains negative for after n = 2652

[2653,*] where * at 4999 the sum is -653126

The conjecture is that it is always negative thereafter.

[1,2]------ [3]
[4,22]----- [23]
[24,28]---- [29,33]
[34]------- [35]
[36,39]---- [40]
[41,45]---- [46,53]
[54,239]--- [240]
[241,303]-- [304,425]
[426]------ [427]
[428]------ [429,532]
[533]------ [534,554]
[555]------ [556,573]
[574,575]---[576,1060]
[1061,1065] [1066]
[1067,1074] [1075,1082]
[1083,1091] [1092,1114]
[1115,1127] [1128,1144]
[1145]----- [1146,1391]
[1392,1400] [1401,1402]
[1403,1411] [1412,1414]
[1415,1455] [1456,1459]
[1460]----- [1461,1472]
[1473,1484] [1485,1681]
[1682,1761] [1762,1766]
[1767]----- [1768,1786]
[1787]----- [1788,1817]
[1818,1830] [1831,2222]
[2223,2283] [2284,2286]
[2287,2292] [2293,2305]
[2306,2310] [2311,2312]
[2313,2382] [2383,2384]
[2385]----- [2386,2393]
[2394,2403] [2404,2407]
[2408,2413] [2414]
[2415,2416] [2417,2423]
[2424,2464] [2465,2468]
[2469,2473] [2474,2606]
[2607]----- [2608,2610]
[2611]----- [2612,2613]
[2614,2631] [2632,2633]
[2634,2638] [2639,2640]
[2641]----- [2642,2652]
[2653,*]
* at 4999 the sum is -653126
* at 6300 the sum is -940962