A074675 -id:A074675 - cp's OEIS frontend

A074670 Differences between successive six-digit distinct-digit primes.

8, 30, 40, 60, 42, 8, 16, 24, 6, 50, 4, 6, 20, 6, 84, 6, 24, 66, 94, 14, 16, 306, 168, 72, 20, 18, 90, 30, 82, 98, 100, 272, 48, 10, 30, 42, 158, 10, 42, 14, 4, 26, 16, 20, 24, 10, 30, 6, 30, 30, 38, 42, 10, 74, 34

Offset: 1

Zak Seidov, Aug 30 2002

There are 10238 terms in this sequence, all of which are in the b-file. - Harvey P. Dale, Jun 06 2018

			a(1)=8 & a(2)=30 because first three 6-digit distinct-digit primes are 102359, 102367, 102397 and differences between them are 8 and 30.

Harvey P. Dale, Table of n, a(n) for n = 1..10238

The first differences of A074669. For 3-digit distinct-digit primes, see A074675, A074676. For 4-digit distinct-digit primes, see A074673, A074674. For 5-digit distinct-digit primes, see A074671, A074672. For 7-digit distinct-digit primes, see A074667, A074668. For 8-digit distinct-digit primes, see A074665, A074666.

a=102345; b=a+8000; se6 = Select[Range[a, b, 2], Length[Union[IntegerDigits[ # ]]] == 6 && PrimeQ[ # ] & ]; Flatten[Table[{se6[[i+1]]-se6[[i]]}, {i, Length[se6]-1}]]
Select[Prime[Range[9593,78498]],Length[Union[IntegerDigits[#]]] == 6&] // Differences (* Harvey P. Dale, Jun 06 2018 *)

A074672 Differences between successive five-digit distinct-digit primes.

Original entry on oeis.org

4, 6, 6, 8, 6, 16, 68, 12, 58, 2, 24, 4, 2, 4, 24, 42, 38, 22, 8, 30, 12, 18, 30, 36, 6, 10, 14, 36, 48, 10, 6, 6, 8, 70, 20, 16, 14, 1050, 6, 6, 24, 24, 250, 32, 30, 28, 20, 16, 6, 8, 10, 6, 36, 8, 22, 14, 6, 48, 10, 6, 6, 30, 8, 6, 36, 4, 20, 46, 44, 40, 14, 46

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 2529 five-digit primes with all distinct digits, so the sequence of differences is finite as well. The end of the sequence is: 42, 18, 80, 42, 30, 10, 38, 22, 38, 22, 30, 38, 162, 28, 2, 18, 156, 24, 6, 10, 66, 20, 64, 6, 38, 6, 60, 4, 6, 20, 60, 46, 14, 6, 34, 36, 18, 2, 10, 48, 6, 14, 72, 18.

			a(1)=4 because the first and second five-digit primes with all distinct digits are 10243, 10247 and difference between them is 4.

Harvey P. Dale, Table of n, a(n) for n = 1..2528 (Complete list of all terms)

The first differences of the A074671. For 3-digit distinct-digit primes, see A074675, A074676. For 4-digit distinct-digit primes, see A074673, A074674. For 6-digit distinct-digit primes, see A074669, A074670. For 7-digit distinct-digit primes, see A074667, A074668. For 8-digit distinct-digit primes, see A074665, A074666.

se=Select[Range[10243, 98731, 2], Length[Union[IntegerDigits[ # ]]]==5&&PrimeQ[ # ]&]; Flatten[Table[{se[[i+1]]-se[[i]]}, {i, 2528}]]
Differences[Select[Prime[Range[PrimePi[10000]+1,PrimePi[99999]]],Max[ DigitCount[ #]] ==1&]] (* Harvey P. Dale, Jul 19 2019 *)

A074674 Differences between successive four-digit distinct-digit primes.

Original entry on oeis.org

10, 14, 6, 18, 6, 4, 140, 12, 10, 20, 4, 6, 8, 10, 20, 40, 42, 14, 4, 2, 10, 14, 6, 24, 4, 2, 4, 30, 20, 6, 18, 12, 4, 14, 10, 2, 18, 10, 20, 36, 4, 12, 14, 30, 6, 24, 6, 34, 24, 20, 6, 6, 28, 66, 14, 30, 22, 14, 10, 6, 12, 2, 4, 2, 48, 6, 10, 26, 130, 32, 6, 4, 6, 14, 10, 8, 28, 20, 22

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 510 four-digit primes with all distinct digits, so the sequence of differences is finite as well.

			a(1)=10 because the first and second four-digit primes with all distinct digits are 1039, 1049 and difference between them is 10.

Harvey P. Dale, Table of n, a(n) for n = 1..509

The first differences of the A074673. For 3-digit distinct-digit primes, see A074675, A074676. For 5-digit distinct-digit primes, see A074671, A074672. For 6-digit distinct-digit primes, see A074669, A074670. For 7-digit distinct-digit primes, see A074667, A074668. For 8-digit distinct-digit primes, see A074665, A074666.

se=Select[Range[1039, 9871, 2], Length[Union[IntegerDigits[ # ]]]==4&&PrimeQ[ # ]&]; Flatten[Table[{se[[i+1]]-se[[i]]}, {i, 509}]]
Differences[Select[Prime[Range[169,1229]],Length[Union[ IntegerDigits[#]]] == 4&]] (* Harvey P. Dale, Oct 11 2015 *)

A073643 Nine-digit primes with all distinct digits.

Original entry on oeis.org

102345689, 102345697, 102345869, 102346789, 102346879, 102346897, 102346957, 102347689, 102348679, 102348769, 102349867, 102354689, 102354697, 102356489, 102356789, 102356987, 102358769, 102358967, 102364859, 102364879, 102365897

Offset: 1

Zak Seidov, Aug 29 2002

The number of distinct-digit primes are finite. E.g. there are exactly 145227 such nine-digit primes from 102345689 to 987654103.

All terms have exactly one "0" because nine-digit zero-less numbers with all distinct digits are divisible by 9. - Zak Seidov, Mar 15 2015

			a(1)=102345689 because 102345689 is the smallest 9-digit prime with all distinct digits.

Zak Seidov, Table of n, a(n) for n = 1..10000

For 3-digit distinct-digit primes, see A074675, A074676.
4-digit distinct-digit primes are in A074673, see also A074674.
5-digit distinct-digit primes are in A074671, see also A074672.
6-digit distinct-digit primes are in A074669, see also A074670.
7-digit distinct-digit primes are in A074667, see also A074668.
8-digit distinct-digit primes are in A074665, see also A074666.

from sympy import isprime
from itertools import permutations as perms
nines = (int("".join(p)) for p in perms("0123456789", 9) if p[0] != "0")
afull = [k for k in nines if isprime(k)]
print(afull[:24]) # Michael S. Branicky, Aug 04 2022

A074676 Differences between consecutive three-digit distinct-digit primes.

Original entry on oeis.org

4, 2, 18, 10, 2, 10, 8, 6, 4, 6, 6, 14, 4, 42, 2, 10, 6, 6, 6, 2, 10, 2, 10, 14, 10, 30, 2, 10, 8, 12, 10, 8, 4, 8, 10, 2, 10, 8, 18, 4, 2, 4, 12, 8, 4, 12, 6, 12, 2, 18, 6, 16, 6, 2, 16, 6, 8, 6, 6, 4, 2, 12, 10, 2, 4, 6, 6, 14, 10, 8, 10, 8, 10, 20, 4, 8, 10, 8, 40, 12, 2, 4, 2, 10, 14, 4, 2

Offset: 1

Zak Seidov, Aug 30 2002

There are exactly 97 three-digit primes with all distinct digits, so the sequence is finite.

			a(1)=4 because the first and the second three-digit primes with all distinct digits are 103, 107 and difference between them is 4.

Jinyuan Wang, Table of n, a(n) for n = 1..96

The first differences of the A074675. For 4-digit distinct-digit primes, see A074673, A074674. For 5-digit distinct-digit primes, see A074671, A074672. For 6-digit distinct-digit primes, see A074669, A074670. For 7-digit distinct-digit primes, see A074667, A074668. For 8-digit distinct-digit primes, see A074665, A074666.

se=Select[Range[103, 983, 2], Length[Union[IntegerDigits[ # ]]]==3&&PrimeQ[ # ]&]; Flatten[Table[{se[[i+1]]-se[[i]]}, {i, 96}]]

A235155 Primes which have one or more occurrences of exactly three different digits.

Original entry on oeis.org

103, 107, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 317, 347, 349, 359, 367, 379, 389, 397, 401, 409, 419, 421, 431, 439, 457, 461, 463, 467, 479, 487, 491, 503, 509, 521, 523, 541, 547

Offset: 1

Colin Barker, Jan 04 2014

The first term having a repeated digit is 1009.

Christopher M. Conrey, Table of n, a(n) for n = 1..10000 (first 2000 terms from Colin Barker)
Christopher M. Conrey, MATLAB Program

Cf. A235154, A235156, A235157, A235158, A235159, A235160, A235161.

Cf. A074675.

MATLAB
```
%See Conrey Link
```

Select[Prime[Range[200]],Count[DigitCount[#],0]==7&] (* Harvey P. Dale, Jul 27 2020 *)

s=[]; forprime(n=100, 1000, if(#vecsort(eval(Vec(Str(n))),,8)==3, s=concat(s, n))); s

A255596 Distinct-digit primes that are the concatenation of m and prime(m) for some number m.

Original entry on oeis.org

23, 47, 613, 1237, 1759, 27103, 35149, 45197, 57269, 58271, 61283, 85439, 93487, 145829, 147853, 2371489, 3152087, 3902687, 4062791, 5614073, 5914327, 7405639, 8356421

Offset: 1

Zak Seidov, Mar 25 2015

			The last term is a(23) = 8356421 (prime) because all 7 digits are different and m=835 with 6421=prime(m).

Cf. A073643, A074665, A074667, A074669, A074671, A074673, A074675, A160402, A256339.

Select[FromDigits[IntegerDigits@ #~Join~IntegerDigits[Prime@ #]] & /@
Range@ 1200, PrimeQ@ # && Max@ DigitCount@ # == 1 &] (* Michael De Vlieger, Mar 25 2015 *)

A256339 Distinct-digit primes that are concatenation of prime(m) and m for some m.

Original entry on oeis.org

53, 239, 6719, 7321, 4073561, 6257813, 6521843, 85271063

Offset: 1

Zak Seidov, Mar 25 2015

The last term is a(8) = 85271063 (prime) because all 8 digits are different and m=1063 with 8527=prime(m).

Subsequence of A029743 (distinct-digit primes).

Cf. A073643, A074665, A074667, A074669, A074671, A074673, A074675, A160402.

Select[FromDigits[IntegerDigits[Prime@ #]~Join~IntegerDigits@ #] & /@
Range@ 1200, PrimeQ@ # && Max@ DigitCount@ # == 1 &] (* Michael De Vlieger, Mar 25 2015 *)

cp's OEIS Frontend

A074670 Differences between successive six-digit distinct-digit primes.

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A074672 Differences between successive five-digit distinct-digit primes.

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A074674 Differences between successive four-digit distinct-digit primes.

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A073643 Nine-digit primes with all distinct digits.

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A074676 Differences between consecutive three-digit distinct-digit primes.

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A235155 Primes which have one or more occurrences of exactly three different digits.

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PARI

A255596 Distinct-digit primes that are the concatenation of m and prime(m) for some number m.

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Mathematica

A256339 Distinct-digit primes that are concatenation of prime(m) and m for some m.

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Mathematica