Counting up in prime numbers #2

BlackTuesday · Post by **BlackTuesday** » 02 Sep 2020 22:20

Next one is also an isolated prime:

115,343

with a prime offset = 683

RogerE · Post by **RogerE** » 03 Sep 2020 01:40

Welcome back to this thread BlackTuesday

Isolated prime:

115,343

/RogerE

BlackTuesday · Post by **BlackTuesday** » 03 Sep 2020 07:27

duplicate message

BlackTuesday · Post by **BlackTuesday** » 03 Sep 2020 07:28

Thanks RogerE

seems the isolated prime refused to move ahead

RogerE · Post by **RogerE** » 03 Sep 2020 12:16

Thank you BlackTuesday

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

BlackTuesday · Post by **BlackTuesday** » 04 Sep 2020 09:04

You're welcome RogerE

Next one is a solo prime

115,399

115,399 = 114660 + 739, and 739 = prime

RogerE · Post by **RogerE** » 04 Sep 2020 22:26

Next an isolated prime

115,421

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

BlackTuesday · Post by **BlackTuesday** » 05 Sep 2020 17:25

An isolated prime again

115,429

115,429 = 114660 + 769, and 769 = prime

RogerE · Post by **RogerE** » 06 Sep 2020 01:15

An isolated prime again

115,459

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

/RogerE

BlackTuesday · Post by **BlackTuesday** » 06 Sep 2020 19:34

This time there are twin primes

115,469

115,471

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

115,471 = 114660 + 811, and 811 = prime

RogerE · Post by **RogerE** » 06 Sep 2020 20:49

An isolated prime again

115,499

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

/RogerE

BlackTuesday · Post by **BlackTuesday** » 08 Sep 2020 19:15

And an isolated prime again

115,513

115,513 = 114660 + 853, and 853 = prime

RogerE · Post by **RogerE** » 09 Sep 2020 00:32

An isolated prime again

115,523

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

/RogerE

BlackTuesday · Post by **BlackTuesday** » 09 Sep 2020 22:02

An isolated prime again

115,547

115,547 = 114660 + 887, and 887 = prime

RogerE · Post by **RogerE** » 10 Sep 2020 01:24

An isolated prime again

115,553

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

BlackTuesday · Post by **BlackTuesday** » 11 Sep 2020 00:35

An isolated prime again

115,561

115,561 = 114660 + 901, and 901 = composite 17 x 53

RogerE · Post by **RogerE** » 11 Sep 2020 04:42

An isolated prime

115,571

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

BlackTuesday · Post by **BlackTuesday** » 12 Sep 2020 01:42

An isolated prime again

115,589

115,589 = 114660 + 929, and 929 = prime

RogerE · Post by **RogerE** » 12 Sep 2020 02:45

Thank you BlackTuesday.
Next:

A maximal group of three primes within a run of seven integers,
comprising twin primes and a near neighbour prime.

(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

115,601 = 114660 + 941, and 941= prime

115,603 = 114660 + 943, and 943 = composite 23 x 41

/RogerE

BlackTuesday · Post by **BlackTuesday** » 13 Sep 2020 02:46

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

Now back to normal, I mean isolated prime again

115,613

115,613 = 114660 + 953, and 953 = prime

RogerE · Post by **RogerE** » 13 Sep 2020 04:03

Isolated prime again

115,631

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

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

BlackTuesday · Post by **BlackTuesday** » 14 Sep 2020 07:09

And isolated prime again

115,637

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

Thanks for the link Roger!

RogerE · Post by **RogerE** » 14 Sep 2020 20:09

Another isolated prime

115,657

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

[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!]

BlackTuesday · Post by **BlackTuesday** » 15 Sep 2020 21:02

And again

115,663

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

Thanks for the memo Roger!

RogerE · Post by **RogerE** » 17 Sep 2020 03:38

Isolated prime

115,679

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

BlackTuesday · Post by **BlackTuesday** » 18 Sep 2020 08:58

Isolated prime

115,693

115,693 = 114660 + 1033, and offset 1033 = prime

RogerE · Post by **RogerE** » 18 Sep 2020 10:32

Isolated prime (like an aeroplane)

115,727

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

BlackTuesday · Post by **BlackTuesday** » 23 Sep 2020 07:22

Here comes the aeroplane again

115,733

115,733 = 114660 + 1073, and offset 1073 = composite 29 x 37

RogerE · Post by **RogerE** » 23 Sep 2020 15:54

Isolated prime, no more planes in sight

115,741

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

RogerE · Post by **RogerE** » 25 Sep 2020 19:47

After two days, here's the next:

Isolated prime

115,751

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

RogerE · Post by **RogerE** » 28 Sep 2020 16:35

After three more days, here's the next:

Isolated prime

115,757

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

RogerE · Post by **RogerE** » 29 Sep 2020 15:33

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

115,763

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

RogerE · Post by **RogerE** » 03 Oct 2020 12:01

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

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

/RogerE

RogerE · Post by **RogerE** » 05 Oct 2020 04:41

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
115,783 = 114660 + 1123, and offset 1123 = prime[/size]

/RogerE

RogerE · Post by **RogerE** » 05 Oct 2020 13:57

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
115,783 = 114660 + 1123, and offset 1123 = prime[/size]

/RogerE

RogerE · Post by **RogerE** » 10 Oct 2020 03:06

115,793

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

/RogerE

RogerE · Post by **RogerE** » 11 Oct 2020 00:40

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

RogerE · Post by **RogerE** » 11 Oct 2020 21:57

115,823

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

/RogerE

RogerE · Post by **RogerE** » 19 Oct 2020 00:03

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

RogerE · Post by **RogerE** » 19 Oct 2020 22:00

115,837

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

/RogerE

BlackTuesday · Post by **BlackTuesday** » 27 Oct 2020 10:07

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

RogerE · Post by **RogerE** » 27 Oct 2020 11:56

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

BlackTuesday · Post by **BlackTuesday** » 28 Oct 2020 08:51

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

RogerE · Post by **RogerE** » 28 Oct 2020 22:15

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

Next prime is
115,891

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

/RogerE

BlackTuesday · Post by **BlackTuesday** » 29 Oct 2020 08:54

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

RogerE · Post by **RogerE** » 29 Oct 2020 09:49

It is interesting to see twin primes both having composite offsets.

(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

BlackTuesday · Post by **BlackTuesday** » 30 Oct 2020 09:06

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

RogerE · Post by **RogerE** » 30 Oct 2020 09:43

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

BlackTuesday · Post by **BlackTuesday** » 01 Nov 2020 09:00

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

RogerE · Post by **RogerE** » 01 Nov 2020 11:22

It's good to have your renewed participation BlackTuesday

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