Strong Prime Calculator

Enter a number to check if it's a strong prime, or provide a range to generate all strong primes within it.

Strong Prime Check or Generate

What is a Strong Prime?

A strong prime is a prime number \( p \) that is greater than the average of its two nearest neighboring primes. In simpler terms, if a prime number is larger than the mean of the prime numbers immediately before and after it, it is classified as a strong prime.

How to Determine if a Number is a Strong Prime

  1. Check Primality: Verify that \( p \) is a prime number.
  2. Find Neighboring Primes: Identify the prime numbers immediately before (\( p_1 \)) and after (\( p_2 \)) \( p \).
  3. Calculate the Average: Compute the mean of the neighboring primes using the formula: \( \text{average} = \frac{p_1 + p_2}{2} \).
  4. Compare: If \( p > \text{average} \), \( p \) is a strong prime; otherwise, it is not.

Examples

Example 1: Is 101 a Strong Prime?

Solution:

Previous prime: 97

Next prime: 103

Average: \( \text{average} = \frac{97 + 103}{2} = 100 \)

Comparison: 101 > 100

Result: 101 is a strong prime.

Example 2: Is 211 a Strong Prime?

Solution:

Previous prime: 199

Next prime: 223

Average: \( \text{average} = \frac{199 + 223}{2} = 211 \)

Comparison: 211 = 211

Result: 211 is not a strong prime.

Example 3: Is 1997 a Strong Prime?

Solution:

Previous prime: 1993

Next prime: 1999

Average: \( \text{average} = \frac{1993 + 1999}{2} = 1996 \)

Comparison: 1997 > 1996

Result: 1997 is a strong prime.

First 100 Strong Primes

  • 11
  • 17
  • 29
  • 37
  • 41
  • 59
  • 67
  • 71
  • 79
  • 97
  • 101
  • 107
  • 127
  • 137
  • 149
  • 163
  • 179
  • 191
  • 197
  • 223
  • 227
  • 239
  • 251
  • 269
  • 277
  • 281
  • 307
  • 311
  • 331
  • 347
  • 367
  • 379
  • 397
  • 419
  • 431
  • 439
  • 457
  • 461
  • 479
  • 487
  • 499
  • 521
  • 541
  • 557
  • 569
  • 587
  • 599
  • 613
  • 617
  • 631
  • 641
  • 659
  • 673
  • 701
  • 719
  • 727
  • 739
  • 751
  • 757
  • 769
  • 787
  • 809
  • 821
  • 827
  • 853
  • 857
  • 877
  • 881
  • 907
  • 929
  • 937
  • 967
  • 991
  • 1009
  • 1019
  • 1031
  • 1049
  • 1061
  • 1087
  • 1091
  • 1117
  • 1151
  • 1163
  • 1181
  • 1213
  • 1229
  • 1249
  • 1277
  • 1289
  • 1297
  • 1301
  • 1319
  • 1361
  • 1399
  • 1423
  • 1427
  • 1447
  • 1451
  • 1471
  • 1481