Block #349,641

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.842 × 10⁹⁶(97-digit number)

58426817019731832766…44419785603685884889

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

5.842 × 10⁹⁶(97-digit number)

58426817019731832766…44419785603685884889

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.842 × 10⁹⁶(97-digit number)

58426817019731832766…44419785603685884891

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.168 × 10⁹⁷(98-digit number)

11685363403946366553…88839571207371769779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.168 × 10⁹⁷(98-digit number)

11685363403946366553…88839571207371769781

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.337 × 10⁹⁷(98-digit number)

23370726807892733106…77679142414743539559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.337 × 10⁹⁷(98-digit number)

23370726807892733106…77679142414743539561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

4.674 × 10⁹⁷(98-digit number)

46741453615785466213…55358284829487079119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.674 × 10⁹⁷(98-digit number)

46741453615785466213…55358284829487079121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

9.348 × 10⁹⁷(98-digit number)

93482907231570932426…10716569658974158239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.348 × 10⁹⁷(98-digit number)

93482907231570932426…10716569658974158241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.869 × 10⁹⁸(99-digit number)

18696581446314186485…21433139317948316479

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.869 × 10⁹⁸(99-digit number)

18696581446314186485…21433139317948316481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★★☆

Rarity

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer