Block #332,383

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/28/2013, 12:13:34 AM · Difficulty 10.1744 · 6,494,921 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b94845c66a9f7bafb560110f533022c215c582c3cb2eabf917aef582e016efea

View on Chainz ↗

Height

#332,383

Difficulty

10.174397

Transactions

Size

725 B

Version

Bits

0a2ca541

Nonce

6,972

Timestamp

12/28/2013, 12:13:34 AM

Confirmations

6,494,921

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

302acc3694be8cc77112164bbfc8e88a08ebd2f6ae91259967bff43947db01de

Transactions (2)

Coinbasebe1fd8e387ee26…0ae3652271d915

1 in → 1 out9.6600 XPM110 B

AeKNrjNj…1NEq95Ta

d0728f02f59284…b60c1191b44bc8

3 in → 2 out3.3030 XPM523 B

AcL2Tqnu…gwHZGbmn AJ9PvRK7…RSKR4o1S

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.

2.383 × 10⁹⁸(99-digit number)

23837951551986598750…65645593641445669629

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

2.383 × 10⁹⁸(99-digit number)

23837951551986598750…65645593641445669629

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.383 × 10⁹⁸(99-digit number)

23837951551986598750…65645593641445669631

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

4.767 × 10⁹⁸(99-digit number)

47675903103973197501…31291187282891339259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.767 × 10⁹⁸(99-digit number)

47675903103973197501…31291187282891339261

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

9.535 × 10⁹⁸(99-digit number)

95351806207946395002…62582374565782678519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.535 × 10⁹⁸(99-digit number)

95351806207946395002…62582374565782678521

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

1.907 × 10⁹⁹(100-digit number)

19070361241589279000…25164749131565357039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.907 × 10⁹⁹(100-digit number)

19070361241589279000…25164749131565357041

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

3.814 × 10⁹⁹(100-digit number)

38140722483178558001…50329498263130714079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.814 × 10⁹⁹(100-digit number)

38140722483178558001…50329498263130714081

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 #332,383

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