A088652
Triangle of primes arising in A088651. The n-th row of the triangle contains set of n primes of the form r*A088651(n)-1 for r = 1 to n. Sequence contains the triangle by rows.
Original entry on oeis.org
2, 2, 5, 3, 7, 11, 5, 11, 17, 23, 5, 11, 17, 23, 29, 154769, 309539, 464309, 619079, 773849, 928619, 2894219, 5788439, 8682659, 11576879, 14471099, 17365319, 20259539, 2894219, 5788439, 8682659, 11576879, 14471099, 17365319, 20259539
Offset: 1
2
2 5
3 7 11
5 11 17 23
5 11 17 23 29
...
The fifth row contains primes 6r-1 for r = 1 to 5 since A088651(5)=6.
A088250
a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.
Original entry on oeis.org
1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870
Offset: 1
a(11) = 1893245380950 because all eleven numbers 1*1893245380950 + 1, 2*1893245380950 + 1, 3*1893245380950 + 1, ..., 10*1893245380950 + 1 & 11*1893245380950 + 1 are prime and 1893245380950 is the smallest number with such property.
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a[n_] := Block[{k = If[n < 4, 1, 6], s}, s = k; While[! AllTrue[k Range[n] + 1, PrimeQ], k += s]; k]; Array[a, 8] (* Giovanni Resta, Mar 31 2017 *)
A125838
a(n) is the smallest number m such that k*m - 1 for k=2,3,...,n is prime.
Original entry on oeis.org
2, 2, 2, 6, 120, 120, 2894220, 397073040, 1236161850, 764907546690, 8955490023480, 138393712627170, 8047290924923250
Offset: 2
a(7)=120 because 2*120-1, 3*120-1, 4*120-1, 5*120-1, 6*120-1 & 7*120-1 are prime and 120 is the smallest such number.
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a[n_] := Block[{k=2}, While[! AllTrue[k Range[2, n] - 1, PrimeQ], k += 2]; k]; a /@
Range[2, 8] (* Giovanni Resta, Mar 29 2017 *)
a(8) from Luke Pebody (luke.pebody(AT)gmail.com)
a(9)-a(10) from Vladimir Trushkov (vladimir(AT)trushkov.botik.ru)
A125839
a(n) is the smallest number m such that k*m - 1 is prime for all k=3,4,...,n.
Original entry on oeis.org
1, 1, 6, 18, 120, 1260, 1485540, 28667100, 28667100, 842889105240, 2281585556250, 163881570370980, 45187548280664790
Offset: 3
Luke Pebody (luke.pebody(AT)gmail.com), Jan 02 2007
a(11)=28667100 because 3*28667100-1, 4*28667100-1, 5*28667100-1, 6*28667100-1, 7*28667100-1, 8*28667100-1, 9*28667100-1, 10*28667100-1 & 11*28667100-1 are prime and 28667100 is the smallest number with this property.
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a[n_] := Block[{k = If[n<5, 1, 6], s}, s = k; While[! AllTrue[k Range[3, n] - 1, PrimeQ], k += s]; k]; a /@ Range[3, 9] (* Giovanni Resta, Mar 29 2017 *)
A101779
a(n) = least k such that all of k, 2k+1, 3k+2, ..., nk+n-1 are primes, or 0 if no such k is found.
Original entry on oeis.org
2, 2, 3, 5, 5, 154769, 2894219, 2894219, 407874179, 214580145779, 9448481062019, 247236503934419, 2545206711847799, 18178612369988250179, 53792264108455702829
Offset: 1
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f[1] = 2; f[n_] := f[n] = Block[{k = PrimePi@ f[n - 1], p, t = Table[i*p + (i - 1), {i, 2, n}]}, While[p = Prime@k; Union@PrimeQ@t != {True}, k++ ]; p]; Do[ Print[f@n // Timing], {n, 10}] (* Robert G. Wilson v, Mar 23 2007 *)
A164325
a(n) is the smallest number m such that (2k-1)m+1 is prime for all 0
Original entry on oeis.org
1, 2, 2, 6, 1170, 64590, 25153800, 25153800, 4747505070, 207187349040, 6703860240000, 26997529639080, 1760354281625940, 1760354281625940, 10718654377787155800
Offset: 1
a(5) corrected by Zak Seidov, Sep 16 2009
A202779
Least k such that x*k - 1 produces primes for x=1..n and composite for x=n+1.
Original entry on oeis.org
8, 3, 4, 1410, 6, 154770, 5246010, 2894220, 407874180, 214580145780, 9448481062020, 247236503934420, 2545206711847800, 18178612369988250180, 53792264108455702830
Offset: 1
- Wacław Sierpiński, Czym sie zajmuje teoria liczb. Warsaw: PW "Wiedza Powszechna", 1957, pp. 88-89.
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Table[k = 3; While[i = 1; While[i <= n && PrimeQ[i*k - 1], i++]; i <= n || PrimeQ[i*k - 1], k++]; k, {n, 8}]
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