Block #245,632

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 2:32:28 PM · Difficulty 9.9640 · 6,564,237 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d7038847a2eb151c1539cfae56404f602e94c3f27d1492ca7eed95912c7f3ff

View on Chainz ↗

Height

#245,632

Difficulty

9.963953

Transactions

Size

1.44 KB

Version

Bits

09f6c59a

Nonce

66,861

Timestamp

11/5/2013, 2:32:28 PM

Confirmations

6,564,237

Mined by

⛏️ RyAPgWZwJ2U1QoyziLCpMHctYYS61nTrECFn

Merkle Root

124fd4efee6f3907d8ec9113c240610afbef226f8d62a48abd6a12c4ca0ee965

Transactions (1)

Coinbase124fd4efee6f39…6a12c4ca0ee965

1 in → 39 out10.0400 XPM1.36 KB

APgWZwJ2…1nTrECFn AU7kLmhQ…qhCn5tjQ ANuKx9Ke…wm7nrBRq AZu2fDvw…7iuq9B9M ALdHh27b…XNbqrvPf

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.

9.380 × 10⁹⁶(97-digit number)

93801291322577760188…96614357217273620479

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

9.380 × 10⁹⁶(97-digit number)

93801291322577760188…96614357217273620479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.380 × 10⁹⁶(97-digit number)

93801291322577760188…96614357217273620481

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

1.876 × 10⁹⁷(98-digit number)

18760258264515552037…93228714434547240959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.876 × 10⁹⁷(98-digit number)

18760258264515552037…93228714434547240961

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

3.752 × 10⁹⁷(98-digit number)

37520516529031104075…86457428869094481919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.752 × 10⁹⁷(98-digit number)

37520516529031104075…86457428869094481921

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

7.504 × 10⁹⁷(98-digit number)

75041033058062208151…72914857738188963839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.504 × 10⁹⁷(98-digit number)

75041033058062208151…72914857738188963841

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

1.500 × 10⁹⁸(99-digit number)

15008206611612441630…45829715476377927679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #245,632

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