Block #331,672

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 12:58:08 PM · Difficulty 10.1683 · 6,462,579 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6cdbe1218aeda57129bad96313b709ca6177756a15f445f0a6df631e5cee1766

View on Chainz ↗

Height

#331,672

Difficulty

10.168271

Transactions

Size

1.04 KB

Version

Bits

0a2b13cd

Nonce

20,340

Timestamp

12/27/2013, 12:58:08 PM

Confirmations

6,462,579

Merkle Root

4b62f3c42f7fc702334a203ba09273bfc21598660285b16a3e422ab54c984c9b

Transactions (1)

Coinbase4b62f3c42f7fc7…422ab54c984c9b

1 in → 27 out9.6600 XPM981 B

AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 AFutDVqJ…TJTJj6UF AVVVLvhX…ShSvqxic AZ2pPuKg…95SN2Yr7

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.

3.141 × 10⁹²(93-digit number)

31417513952666488494…45706046325521040999

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

3.141 × 10⁹²(93-digit number)

31417513952666488494…45706046325521040999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.141 × 10⁹²(93-digit number)

31417513952666488494…45706046325521041001

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

6.283 × 10⁹²(93-digit number)

62835027905332976989…91412092651042081999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.283 × 10⁹²(93-digit number)

62835027905332976989…91412092651042082001

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

1.256 × 10⁹³(94-digit number)

12567005581066595397…82824185302084163999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.256 × 10⁹³(94-digit number)

12567005581066595397…82824185302084164001

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

2.513 × 10⁹³(94-digit number)

25134011162133190795…65648370604168327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.513 × 10⁹³(94-digit number)

25134011162133190795…65648370604168328001

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

5.026 × 10⁹³(94-digit number)

50268022324266381591…31296741208336655999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.026 × 10⁹³(94-digit number)

50268022324266381591…31296741208336656001

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