Block #490,956

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 5:02:15 AM · Difficulty 10.6794 · 6,318,607 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

cefed848e1cdb0e47a1fc2c96a00d8c31c64d85151a08185975a8b45147453af

View on Chainz ↗

Height

#490,956

Difficulty

10.679375

Transactions

Size

1.92 KB

Version

Bits

0aadeb8d

Nonce

123,266

Timestamp

4/14/2014, 5:02:15 AM

Confirmations

6,318,607

Mined by

⛏️ P2SHAVUSTGLfXSGYjUDuVVpW48qmaeSeYSsAGR

Merkle Root

daad20b4db7bc542fb33618772d7fd77051c3c4b1b26bff4087c56d5b7fa5420

Transactions (2)

Coinbase5a3f44233facf3…66e5ef9a1aadac

1 in → 1 out8.7700 XPM109 B

AVUSTGLf…SeYSsAGR

ce79162ea4e423…9c5a029840ef0d

5 in → 30 out44.2700 XPM1.73 KB

APQCLq5D…cpNbYpoy AUkdqaxr…4jcbMUQ7 AQsqCMcB…YxgrjJnb AYxRMkrV…4xUzBCzM AKzv8KjF…W6FeM9j1

Prime Chain Origin

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.

2.561 × 10⁹⁸(99-digit number)

25616588704957285316…38078507253215672469

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

2.561 × 10⁹⁸(99-digit number)

25616588704957285316…38078507253215672469

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.561 × 10⁹⁸(99-digit number)

25616588704957285316…38078507253215672471

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

5.123 × 10⁹⁸(99-digit number)

51233177409914570633…76157014506431344939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.123 × 10⁹⁸(99-digit number)

51233177409914570633…76157014506431344941

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

1.024 × 10⁹⁹(100-digit number)

10246635481982914126…52314029012862689879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.024 × 10⁹⁹(100-digit number)

10246635481982914126…52314029012862689881

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

2.049 × 10⁹⁹(100-digit number)

20493270963965828253…04628058025725379759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.049 × 10⁹⁹(100-digit number)

20493270963965828253…04628058025725379761

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

4.098 × 10⁹⁹(100-digit number)

40986541927931656506…09256116051450759519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.098 × 10⁹⁹(100-digit number)

40986541927931656506…09256116051450759521

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

Block #490,956

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