Block #345,334

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/5/2014, 8:58:19 PM · Difficulty 10.2091 · 6,470,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec31c8fd9431088ddcfcedb6fdcdac92fe8c145c4cd61761c6bd507926611ad7

View on Chainz ↗

Height

#345,334

Difficulty

10.209080

Transactions

Size

936 B

Version

Bits

0a358642

Nonce

578,955

Timestamp

1/5/2014, 8:58:19 PM

Confirmations

6,470,580

Mined by

⛏️ DaR"gAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

9dad8810dcae9f7c7813aae07e8ee176ba6b093dd3945399cdae68adcf3e974b

Transactions (1)

Coinbase9dad8810dcae9f…ae68adcf3e974b

1 in → 23 out9.5800 XPM845 B

AQwRN8bE…V8PsTcY9 AL8CJrXc…ReWqhicJ AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz Ac3NX3Zf…iwsujMjK

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.

2.906 × 10⁹⁷(98-digit number)

29061552973607376304…61436827600714286079

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

2.906 × 10⁹⁷(98-digit number)

29061552973607376304…61436827600714286079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.906 × 10⁹⁷(98-digit number)

29061552973607376304…61436827600714286081

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

5.812 × 10⁹⁷(98-digit number)

58123105947214752609…22873655201428572159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.812 × 10⁹⁷(98-digit number)

58123105947214752609…22873655201428572161

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

1.162 × 10⁹⁸(99-digit number)

11624621189442950521…45747310402857144319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.162 × 10⁹⁸(99-digit number)

11624621189442950521…45747310402857144321

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

2.324 × 10⁹⁸(99-digit number)

23249242378885901043…91494620805714288639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.324 × 10⁹⁸(99-digit number)

23249242378885901043…91494620805714288641

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

4.649 × 10⁹⁸(99-digit number)

46498484757771802087…82989241611428577279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.649 × 10⁹⁸(99-digit number)

46498484757771802087…82989241611428577281

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 #345,334

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