Counting up in prime numbers #2

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BlackTuesday
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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Thanks Roger! :)

And an isolated prime again:

116,027

116,027 = 114660 + 1367, and offset 1367 = prime
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Re: Counting up in prime numbers #2

Post by RogerE »

Another isolated prime:

116,041

116,041 = 114,660 + 1381, with offset 1381 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

And another isolated prime: :)

116,047

116,047 = 114,660 + 1387, with offset 1387 = 19x73 both of which are prime
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Re: Counting up in prime numbers #2

Post by RogerE »

Another isolated prime:

116,089

116,089 = 114,660 + 1429, with offset 1429 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

Next we have twin primes:

116,099
116,101

116,099 = 114,660 + 1439, with offset 1439 = prime
116,101 = 114,660 + 1441, with offset 1441 = composite, 11 x 131

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

An isolated prime (but not too isolated — prime real estate nearby
on either side...

116,107

116,107 = 114,660 + 1447, with offset 1447 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

An isolated prime:

116,113

116,113 = 114,660 + 1453, with offset 1453 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Back! :)

An isolated prime again:

116,131


116,131 = 114,660 + 1471, with offset 1471 = prime
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Re: Counting up in prime numbers #2

Post by RogerE »

Welcome back, BlackTuesday ! :)

An isolated prime again:

116,141


116,141 = 114,660 + 1481, with offset 1481 = prime

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Thanks Roger! :)

And an isolated prime again:

116,159

116,159 = 114,660 + 1499, with offset 1499 = prime
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Re: Counting up in prime numbers #2

Post by RogerE »

Another isolated prime:

116,167

116,167 = 114,660 + 1507, with composite offset 1507 = 11 x 137.

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Another isolated prime: :)

116,177

116,177 = 114,660 + 1517, and offset 1517 = composite of 37 x 41
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Re: Counting up in prime numbers #2

Post by RogerE »

A note about the previous offset, 1517 = composite of 37 x 41

1517 = 1521 - 4 = 39^2 - 2^2, a difference of two squares.
Since a^2 - b^2 = (a - b) x (a + b), we can always factorise such a number :D
In this instance, 1517 = (39 - 2) x (39 + 2) = 37 x 41.

A related note: 40^2 - 39^2 = 40 + 39, so 39^2 = 1600 - 79 = 1521 :D
_____________________________________________
Now for the next primes, a pair of twins.

116,189
116,191

116,189 = 114,660 + 1529, and offset 1529 = composite of 11 x 139
116,191 = 114,660 + 1531, and offset 1531 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Thanks for the interesting notes, Roger! :)

Next is another isolated prime: :)

116,201

116,201 = 114,660 + 1541, and offset 1541 = composite of 23 x 67
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Re: Counting up in prime numbers #2

Post by RogerE »

Next a big gap, then a pair of near twins:

116,239
116,243

116,239 = 114,660 + 1579, and offset 1579 is prime
116,243 = 114,660 + 1583, and offset 1583 is prime


/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Next is an isolated prime: :)

116,257

116,257 = 114,660 + 1597, and offset 1597 = prime
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Re: Counting up in prime numbers #2

Post by RogerE »

Next another pair of near twin primes: :)

116,269
116,273

The offsets this time are also a pair of near twin primes:
116,269 = 114,660 + 1609, and offset 1609 = prime
116,273 = 114,660 + 1613, and offset 1613 = prime


/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Next is an isolated prime: :)

116,279

116,279 = 114,660 + 1619, and offset 1619 = prime
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Re: Counting up in prime numbers #2

Post by RogerE »

Next is a very isolated prime:

116,293

116,293 = 114,660 + 1633, and composite offset 1633 = 23 x 71

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

Next is an isolated prime:

116,329

116,329 = 114,660 + 1669, and offset 1669 = prime

/RogerE :D

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