Block #567,663

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.

1.107 × 10⁹⁷(98-digit number)

11074944908997184345…15757549807418841719

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

1.107 × 10⁹⁷(98-digit number)

11074944908997184345…15757549807418841719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.107 × 10⁹⁷(98-digit number)

11074944908997184345…15757549807418841721

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

2.214 × 10⁹⁷(98-digit number)

22149889817994368690…31515099614837683439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.214 × 10⁹⁷(98-digit number)

22149889817994368690…31515099614837683441

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

4.429 × 10⁹⁷(98-digit number)

44299779635988737381…63030199229675366879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.429 × 10⁹⁷(98-digit number)

44299779635988737381…63030199229675366881

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

8.859 × 10⁹⁷(98-digit number)

88599559271977474763…26060398459350733759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.859 × 10⁹⁷(98-digit number)

88599559271977474763…26060398459350733761

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

1.771 × 10⁹⁸(99-digit number)

17719911854395494952…52120796918701467519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.771 × 10⁹⁸(99-digit number)

17719911854395494952…52120796918701467521

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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