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


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

Also, Milton provides some graphs for handy visualisation,
They show the decrease into 1000 unit steps.

diff1000.docx
diff2000.docx
diff3000.docx
diff4000.docx
diff5000.docx
diff6000.docx




A000171 Prime Curios! Prime Puzzle
Wikipedia 171 Le nombre 171














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