**115,343**

with a prime offset = 683

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- BlackTuesday
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Next one is also an isolated prime:

**115,343**

with a prime offset = 683

with a prime offset = 683

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Welcome back to this thread **BlackTuesday**

Isolated prime:

**115,343**

/RogerE

Isolated prime:

/RogerE

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Last edited by BlackTuesday on 03 Sep 2020 07:29, edited 1 time in total.

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Thanks **RogerE**

seems the isolated prime refused to move ahead

seems the isolated prime refused to move ahead

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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

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 = 114660 + 701, and 701 = prime

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

/RogerE

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You're welcome **RogerE**

Next one is a solo prime

**115,399**

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

Next one is a solo prime

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

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Next an isolated prime

**115,421**

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

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

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An isolated prime again

**115,429**

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

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

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An isolated prime again

**115,459**

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

/RogerE

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

/RogerE

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This time there are twin primes

115,469

115,471

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

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

115,469

115,471

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

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

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An isolated prime again

**115,499**

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

/RogerE

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

/RogerE

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And an isolated prime again

**115,513**

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

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

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An isolated prime again

**115,523**

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

/RogerE

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

/RogerE

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An isolated prime again

**115,547**

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

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

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An isolated prime again

**115,553**

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

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

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An isolated prime again

**115,561**

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

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

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An isolated prime

**115,571**

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

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

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An isolated prime again

**115,589**

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

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

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

- RogerE
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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

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 = 114660 + 937, and 937 = prime

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

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

/RogerE

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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

Now back to normal, I mean isolated prime again

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

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

- RogerE
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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

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

https://en.wikipedia.org/wiki/Prime_number_theorem

/RogerE

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And isolated prime again

115,637

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

Thanks for the link Roger!

115,637

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

Thanks for the link Roger!

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

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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!]

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!]

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And again

**115,663**

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

Thanks for the memo Roger!

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

Thanks for the memo Roger!

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

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Isolated prime

**115,679**

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

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

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Isolated prime

**115,693**

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

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

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

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Isolated prime (like an aeroplane)

**115,727**

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

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

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Here comes the aeroplane again

**115,733**

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

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

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

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Isolated prime, no more planes in sight

**115,741**

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

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

- RogerE
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After two days, here's the next:

Isolated prime

**115,751**

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

Isolated prime

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

- RogerE
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After three more days, here's the next:

Isolated prime

**115,757**

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

Isolated prime

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

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

**115,763**

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

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

- RogerE
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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

After four days, here's a pair of twin primes

And this time there is interest in the offsets!

115,769 = 114660 + 1109, and offset 1109 = prime

115,771 = 114660 + 1111, and offset

/RogerE

- RogerE
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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

The offsets:

115,777 = 114660 + 1117, and offset 1117 = prime

115,781 = 114660 + 1121, and offset

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

/RogerE

- RogerE
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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

At least the offsets were correct!

115,777 = 114660 + 1117, and offset 1117 = prime

115,781 = 114660 + 1121, and offset

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

/RogerE

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

/RogerE

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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

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

115,811 = 114660 + 1133, and offset 1151 = prime

/RogerE

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

/RogerE

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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

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

/RogerE

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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

Next ones are near twins:

115,853

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

115,853 = 114660 + 1193, and offset 1193 = prime

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

- RogerE
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Next two actual twins:

115,861

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

115,861 = 114660 + 1201, and offset 1201 = prime

/RogerE

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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

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

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

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

- RogerE
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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

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 = 114660 + 1231, and offset 1231 = prime

/RogerE

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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

The next ones are:

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

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

- RogerE
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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

(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!

115,933

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

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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

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

Looks like offset 1331 is not far away

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

- RogerE
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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

unusually crowded configurations recently)

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

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

Now, a solo prime for a change

115,987 = 114660 + 1327, and offset 1327 = prime

Not totally absent, but due to workload currently in mini sabbatical mode on the board!

- RogerE
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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

And now another isolated prime.

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

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