## Re: [PrimeNumbers] Euler Totient Result

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• ... I suggest you get a math program (like PARI/GP used below) and do some quick experimenting before publishing alleged theorems. ? {for(n=2,1000,
Message 1 of 2 , Jul 8, 2008
Sebastian Martin wrote:
> Can anyone prove the following result?
> THEOREM:
> 1/2< Phi(p(n+1)+pn)/Phi(pn+p(n-1)) <=2

I suggest you get a math program (like PARI/GP used below)
and do some quick experimenting before publishing alleged theorems.

? {for(n=2,1000,
a=eulerphi(prime(n+1)+prime(n));
b=eulerphi(prime(n)+prime(n-1));
r=a/b;
if(r <= 1/2 | r > 2,
print(prime(n-1)", "prime(n)", "prime(n+1)": "a"/"b" = "r*1.0)
))}
653, 659, 661: 320/640 = 0.500000000000000000
1319, 1321, 1327: 1320/640 = 2.06250000000000000
2297, 2309, 2311: 960/1932 = 0.496894409937888199
2333, 2339, 2341: 1152/2304 = 0.500000000000000000
2339, 2341, 2347: 2336/1152 = 2.02777777777777778
2963, 2969, 2971: 1440/2964 = 0.485829959514170040
3881, 3889, 3907: 3896/1728 = 2.25462962962962963
5273, 5279, 5281: 2560/5272 = 0.485584218512898331
5443, 5449, 5471: 2304/4656 = 0.494845360824742268
5849, 5851, 5857: 5852/2880 = 2.03194444444444444
6263, 6269, 6271: 2880/5760 = 0.500000000000000000
6269, 6271, 6277: 6272/2880 = 2.17777777777777778
7417, 7433, 7451: 7320/3600 = 2.03333333333333333
7583, 7589, 7591: 3520/7584 = 0.464135021097046414
7589, 7591, 7603: 7420/3520 = 2.10795454545454545
7741, 7753, 7757: 3680/7560 = 0.486772486772486773

--
Jens Kruse Andersen
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