## Extended Ulam Spiral

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• I have extended the Ulam Spiral by starting with a prime number (at the center). Then a large number of primes are on the NW corner values. For 101 at the
Message 1 of 2 , Jun 4, 2009
I have extended the Ulam Spiral by starting with
a prime number (at the center). Then a large
number of primes are on the NW corner values.
For 101 at the center yields the numbers:

101,103,113,131,157,191,233,283,(341),(407),(481),
563,653,751,857,971,1093,1223,1361,(1507)

yielding 16/20 primes

The formula is 4n^2-10n+107

Milton L. Brown
miltbrown@...
• Following are the ratios of primes to total for Extended Ulam Spiral 107: 30 .8 40 .78 50 .72 60 .67 70 .63 80 .65 90 .63 100 .64 110 .63 Does this
Message 2 of 2 , Jun 5, 2009
Following are the ratios of primes to total

for Extended Ulam Spiral 107:

30 .8

40 .78

50 .72

60 .67

70 .63

80 .65

90 .63

100 .64

110 .63

Does this remain above 50% ?

I would call {n =1..., 4n^2-10n+107} a dense set of primes?

Milton L. Brown

miltbrown@...
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