Block #335,674

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/30/2013, 10:16:45 AM · Difficulty 10.1445 · 6,474,128 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa798d6db6531c33e8b39f699258c34ba9b23466b8371d0d54b8442c178f94f0

View on Chainz ↗

Height

#335,674

Difficulty

10.144507

Transactions

Size

1.05 KB

Version

Bits

0a24fe63

Nonce

54,963

Timestamp

12/30/2013, 10:16:45 AM

Confirmations

6,474,128

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

28f5062c847fe6a74a7c1d9c6c7c9bfc33fff54b5b06849a5b90ddf0673e3c1a

Transactions (2)

Coinbase1b9609a1c744ac…54a4e6e71643fb

1 in → 1 out9.7100 XPM110 B

AeKNrjNj…1NEq95Ta

47914f6f611b8d…14f741b2a962ff

4 in → 12 out38.7874 XPM873 B

AZQ6NjvC…3Q6hE6gt AX5CTNNa…uc3HTtti AMtFj3PU…ZX4k1cpy AWP3nWpc…wKY1EyHx AJTnJPkG…6HTSvS8F

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.

7.016 × 10¹¹⁰(111-digit number)

70165985393708885559…68257783479788150339

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

7.016 × 10¹¹⁰(111-digit number)

70165985393708885559…68257783479788150339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.016 × 10¹¹⁰(111-digit number)

70165985393708885559…68257783479788150341

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

1.403 × 10¹¹¹(112-digit number)

14033197078741777111…36515566959576300679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.403 × 10¹¹¹(112-digit number)

14033197078741777111…36515566959576300681

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

2.806 × 10¹¹¹(112-digit number)

28066394157483554223…73031133919152601359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.806 × 10¹¹¹(112-digit number)

28066394157483554223…73031133919152601361

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

5.613 × 10¹¹¹(112-digit number)

56132788314967108447…46062267838305202719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.613 × 10¹¹¹(112-digit number)

56132788314967108447…46062267838305202721

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

1.122 × 10¹¹²(113-digit number)

11226557662993421689…92124535676610405439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.122 × 10¹¹²(113-digit number)

11226557662993421689…92124535676610405441

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 #335,674

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