Counting up in prime numbers #2

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Next one is also an isolated prime: :)

115,343

with a prime offset = 683 :D
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Re: Counting up in prime numbers #2

Post by RogerE »

Welcome back to this thread BlackTuesday :D

Isolated prime:

115,343

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

duplicate message
Last edited by BlackTuesday on 03 Sep 2020 07:29, edited 1 time in total.
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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Thanks RogerE :D

seems the isolated prime refused to move ahead :D
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Re: Counting up in prime numbers #2

Post by RogerE »

Thank you BlackTuesday :D
It seems that I was distracted at the time of that post.
Now we have a proper update, with a pair of twin primes:

115,361
115,363

115,361 = 114660 + 701, and 701 = prime
115,363 = 114660 + 703, and 703 = composite 19 x 37

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

You're welcome RogerE :D

Next one is a solo prime

115,399

115,399 = 114660 + 739, and 739 = prime :)
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Re: Counting up in prime numbers #2

Post by RogerE »

Next an isolated prime

115,421

115,421 = 114660 + 761, and 761 = prime :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

An isolated prime again

115,429

115,429 = 114660 + 769, and 769 = prime :D
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Re: Counting up in prime numbers #2

Post by RogerE »

An isolated prime again

115,459

115,459 = 114660 + 799, and 799 = composite 17 x 47 :D

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

This time there are twin primes :D

115,469

115,471


115,469 = 114660 + 809, and 809 = prime :D

115,471 = 114660 + 811, and 811 = prime :D
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Re: Counting up in prime numbers #2

Post by RogerE »

An isolated prime again

115,499

115,499 = 114660 + 839, and 839 = prime :D

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

And an isolated prime again :D

115,513

115,513 = 114660 + 853, and 853 = prime :D
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Re: Counting up in prime numbers #2

Post by RogerE »

An isolated prime again

115,523

115,523 = 114660 + 863, and 863 = prime :D

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

An isolated prime again :D

115,547

115,547 = 114660 + 887, and 887 = prime :D
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Re: Counting up in prime numbers #2

Post by RogerE »

An isolated prime again :D

115,553

115,553 = 114660 + 893, and 893 = composite 19 x 47 :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

An isolated prime again :D

115,561

115,561 = 114660 + 901, and 901 = composite 17 x 53 :D
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Re: Counting up in prime numbers #2

Post by RogerE »

An isolated prime :D

115,571

115,571 = 114660 + 901, and 911 = prime :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

An isolated prime again :D

115,589

115,589 = 114660 + 929, and 929 = prime :D
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Re: Counting up in prime numbers #2

Post by RogerE »

Thank you BlackTuesday.
Next:

A maximal group of three primes within a run of seven integers,
comprising twin primes and a near neighbour prime. :D
(Four consecutive odd numbers must include a multiple of 3,
so when the smallest is greater than 3, at most three of them
can be prime.)

115,597
115,601
115,603

115,597 = 114660 + 937, and 937 = prime :D
115,601 = 114660 + 941, and 941= prime :D
115,603 = 114660 + 943, and 943 = composite 23 x 41 :D

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Wow Roger, thats quite a handful after a long-time :D

Now back to normal, I mean isolated prime again :D

115,613

115,613 = 114660 + 953, and 953 = prime :D
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Re: Counting up in prime numbers #2

Post by RogerE »

Isolated prime again :D

115,631

115,631 = 114660 + 971, and 971 = prime :D

Yes, part of the interest in the primes is their local variability, while their statistical distribution
is tightly constrained.
A Wikipedia article gives considerable detail:
https://en.wikipedia.org/wiki/Prime_number_theorem

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

And isolated prime again :D

115,637


115,637 = 114660 + 977, and 977 = prime :D

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Re: Counting up in prime numbers #2

Post by RogerE »

Another isolated prime :D

115,657

115,657 = 114660 + 997, and offset 997 = prime :D

[Memo: 1331 is the smallest *possible* composite offset
which is a product of more than two prime factors. In fact,
it doesn't yield a prime!]

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

And again :D

115,663

115,663 = 114660 + 1003, and 1003 = composite 17 x 59 :D

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Re: Counting up in prime numbers #2

Post by RogerE »

Isolated prime :D

115,679

115,679 = 114660 + 1019, and offset 1019 = prime :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Isolated prime :D

115,693

115,693 = 114660 + 1033, and offset 1033 = prime :D
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Re: Counting up in prime numbers #2

Post by RogerE »

Isolated prime (like an aeroplane) :D

115,727

115,727 = 114660 + 1067, and offset 1067 = composite 11 x 97 :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Here comes the aeroplane again :D

115,733

115,733 = 114660 + 1073, and offset 1073 = composite 29 x 37 :D
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Re: Counting up in prime numbers #2

Post by RogerE »

Isolated prime, no more planes in sight :D

115,741

115,741 = 114660 + 1081, and offset 1081 = composite 23 x 47 :D

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Re: Counting up in prime numbers #2

Post by RogerE »

After two days, here's the next:

Isolated prime :D

115,751

115,751 = 114660 + 1091, and offset 1091 = prime :D

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Re: Counting up in prime numbers #2

Post by RogerE »

After three more days, here's the next:

Isolated prime :D

115,757

115,757 = 114660 + 1097, and offset 1097 = prime :D

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Re: Counting up in prime numbers #2

Post by RogerE »

After another day, here's the next, another isolated prime :D

115,763

115,763 = 114660 + 1103, and offset 1103 = prime :D

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Re: Counting up in prime numbers #2

Post by RogerE »

Hmmm, where have all the flowers (and followers) gone?
After four days, here's a pair of twin primes :D

115,769
115,771

And this time there is interest in the offsets!

115,769 = 114660 + 1109, and offset 1109 = prime
115,771 = 114660 + 1111, and offset 1111 = composite 11 x 101 :D

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

A maximal set of 3 primes in 4 consecutive odd numbers:

115,777
115,181
115,183

The offsets:

115,777 = 114660 + 1117, and offset 1117 = prime
115,781 = 114660 + 1121, and offset 1121 = composite 19 x 59 :D
115,783 = 114660 + 1123, and offset 1123 = prime[/size]

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

Well. typos excepted! That should have been

115,777
115,781
115,783

At least the offsets were correct!

115,777 = 114660 + 1117, and offset 1117 = prime
115,781 = 114660 + 1121, and offset 1121 = composite 19 x 59 :D
115,783 = 114660 + 1123, and offset 1123 = prime[/size]

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

115,793

115,793 = 114660 + 1133, and offset 1133 = composite 11 x 103

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

Near twins:

115,807
115,811

115,807 = 114660 + 1133, and offset 1147 = composite 31 x 37 =34^2 – 3^2
115,811 = 114660 + 1133, and offset 1151 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

115,823

115,811 = 114660 + 1163, and offset 1163 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

115,831

115,831 = 114660 + 1171, and offset 1171 = prime

Correction: The offset note in the previous post should be
115,823 = 114660 + 1163, and offset 1163 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by RogerE »

115,837

115,837 = 114660 + 1177, and offset 1177 = composite 11 x 107

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

I'm back! ... Thanks RogerE!

Next ones are near twins:

115,849

115,853


115,849 = 114660 + 1189, and offset 1189 = composite of 29 x 41

115,853 = 114660 + 1193, and offset 1193 = prime
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Re: Counting up in prime numbers #2

Post by RogerE »

Welcome back BlackTuesday! We missed you for a while.

Next two actual twins:

115,859

115,861


115,859 = 114660 + 1199, and offset 1199 = composite of 11 x 109
115,861 = 114660 + 1201, and offset 1201 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Thanks Roger! ... I'm glad to be back :)

Aaaaaaand the next is a maximal configuration (4 primes in a run of eleven) :)

115,873

115,877

115,879

115,883


115,873 = 114660 + 1213, and offset 1213 = prime
115,877 = 114660 + 1217, and offset 1217 = prime
115,879 = 114660 + 1219, and offset 1219 = composite of 23 x 53
115,883 = 114660 + 1223, and offset 1223 = prime
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Re: Counting up in prime numbers #2

Post by RogerE »

Nice work BlackTuesday !
Any six consecutive odd numbers must contain two multiples of 3, so at most four
of them can be prime numbers. :D

Next prime is
115,891

115,891 = 114660 + 1231, and offset 1231 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

Thanks Roger!

The next ones are:

115,901

115,903


115,901 = 114660 + 1241, and offset 1241 = composite of 17 x 73
115,903 = 114660 + 1243, and offset 1243 = composite of 11 x 113
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Re: Counting up in prime numbers #2

Post by RogerE »

It is interesting to see twin primes both having composite offsets. :D
(As we approach offsets of 11^3 = 1331 or more, the possibility of composite offsets
which are the product of three primes will exist, though it will be some time before
an actual example is encountered...)

Another pair of twin primes with composite offsets!

115,931

115,933


115,931 = 114660 + 1271, and offset 1271 = composite of 31 x 41
115,933 = 114660 + 1273, and offset 1273 = composite of 19 x 67

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

A solo prime next, for a change :)

115,963

115,963 = 114660 + 1303, and offset 1303 = prime

Looks like offset 1331 is not far away :)
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Re: Counting up in prime numbers #2

Post by RogerE »

Twin primes again — we've been seeing some
unusually crowded configurations recently)

115,979
115,981

Offsets this time are another pair of twin primes:
115,979 = 114660 + 1319, and offset 1319 = prime
115,981 = 114660 + 1321, and offset 1321 = prime

/RogerE :D

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Re: Counting up in prime numbers #2

Post by BlackTuesday »

RogerE wrote:
30 Oct 2020 09:43
....

we've been seeing some
unusually crowded configurations recently)

...
So true! ... I've been thinking that too :)

Now, a solo prime for a change :)

115,987

115,987 = 114660 + 1327, and offset 1327 = prime
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Re: Counting up in prime numbers #2

Post by RogerE »

It's good to have your renewed participation BlackTuesday :D

And now another isolated prime.

116,009

Offset this time exceeds 1331 = 11^3, but still has two prime factors:

116,009 = 114660 + 1349, and offset 1349 = composite, 19 x 71.

/RogerE :D

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