Consider the quadratic:
n^2 + an + b.
Consider integer coefficients a and b in the range:
|a|< 1000, |b| ≤ 1000.
For what values of a and b will the expression produce the maximum number of primes for consecutive values of n, starting with n=0? (Project Euler problem 27)
mx=0;
for a=-1000:1000
for b=-1000:1000
pset=[];
for n=0:9999999
v=n^2+a*n+b;
if v<0
break
end
if ~isprime(v)
break
end
pset(end+1)=v;
end
if length(pset)>mx
disp([length(pset) a b])
mx=length([pset]);
end
end
end
a=-61; b= 971;
for n=0:9999999
v=n^2+a*n+b;
if v<0
break
end
if ~isprime(v)
break
end
fprintf('%3d %5d
',n, v)
end
largest #
so far
a b
1 -1000 2
2 -996 997
3 -499 997
4 -325 977
5 -245 977
6 -197 983
7 -163 983
8 -131 941
9 -121 947
11 -105 967
71 -61 971
For a=-61 b= 971:
n prime
value
0 971
1 911
2 853
3 797
4 743
5 691
6 641
7 593
8 547
9 503
10 461
11 421
12 383
13 347
14 313
15 281
16 251
17 223
18 197
19 173
20 151
21 131
22 113
23 97
24 83
25 71
26 61
27 53
28 47
29 43
30 41
31 41
32 43
33 47
34 53
35 61
36 71
37 83
38 97
39 113
40 131
41 151
42 173
43 197
44 223
45 251
46 281
47 313
48 347
49 383
50 421
51 461
52 503
53 547
54 593
55 641
56 691
57 743
58 797
59 853
60 911
61 971
62 1033
63 1097
64 1163
65 1231
66 1301
67 1373
68 1447
69 1523
70 1601
Edited on February 7, 2024, 3:43 pm
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Posted by Charlie
on 2024-02-07 14:34:58 |
computer solution
