Block #328,662

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 11:00:56 AM · Difficulty 10.1655 · 6,481,525 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

304f80939d0f1463dea745f5dd957cb8be5b13dda926a5d9011fa6f57597cf6f

View on Chainz ↗

Height

#328,662

Difficulty

10.165453

Transactions

Size

935 B

Version

Bits

0a2a5b1a

Nonce

208,434

Timestamp

12/25/2013, 11:00:56 AM

Confirmations

6,481,525

Mined by

⛏️ aRt1AFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

c382e6231cb22b1750884e65b0b8987a8e6d75b07cd5e6aad930261417491c16

Transactions (1)

Coinbasec382e6231cb22b…30261417491c16

1 in → 23 out9.6600 XPM845 B

AFutDVqJ…TJTJj6UF Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AWWfPZBr…fyYrQLSx AYz2ToHc…agXmeuEc

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.

3.174 × 10⁹⁵(96-digit number)

31748916060158467230…52064757657622083319

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

3.174 × 10⁹⁵(96-digit number)

31748916060158467230…52064757657622083319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.174 × 10⁹⁵(96-digit number)

31748916060158467230…52064757657622083321

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

6.349 × 10⁹⁵(96-digit number)

63497832120316934460…04129515315244166639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.349 × 10⁹⁵(96-digit number)

63497832120316934460…04129515315244166641

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

1.269 × 10⁹⁶(97-digit number)

12699566424063386892…08259030630488333279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.269 × 10⁹⁶(97-digit number)

12699566424063386892…08259030630488333281

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

2.539 × 10⁹⁶(97-digit number)

25399132848126773784…16518061260976666559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.539 × 10⁹⁶(97-digit number)

25399132848126773784…16518061260976666561

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

5.079 × 10⁹⁶(97-digit number)

50798265696253547568…33036122521953333119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.079 × 10⁹⁶(97-digit number)

50798265696253547568…33036122521953333121

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 #328,662

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