Block #343,549

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 6:17:31 PM · Difficulty 10.1786 · 6,452,225 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd0d014981e552223af6b0daaf103efa1b60b4c098cfaec55e11b7b14d321e44

View on Chainz ↗

Height

#343,549

Difficulty

10.178600

Transactions

Size

651 B

Version

Bits

0a2db8b6

Nonce

14,891

Timestamp

1/4/2014, 6:17:31 PM

Confirmations

6,452,225

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a2a45b19346bd0554773f21eecb8c54a19c48cf5fc67d860cd9924dde8758d57

Transactions (3)

Coinbaseed5656a7804b33…41e6911c6b568d

1 in → 1 out9.6700 XPM110 B

AeKNrjNj…1NEq95Ta

547cc0c3e51b64…58f5a6d6b2446f

1 in → 2 out1.5936 XPM227 B

AXtrCqGg…zXFA2uhx Ac4bd9PH…E7WVd9nF

bd6792c53d159d…d82a956c0c859f

1 in → 2 out0.0644 XPM226 B

AWKhcKD1…AK1RJ4a3 AY8SeCMB…itqGVCpj

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.

3.167 × 10⁹⁰(91-digit number)

31677376837298771579…83236907587407027789

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

3.167 × 10⁹⁰(91-digit number)

31677376837298771579…83236907587407027789

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.167 × 10⁹⁰(91-digit number)

31677376837298771579…83236907587407027791

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

6.335 × 10⁹⁰(91-digit number)

63354753674597543158…66473815174814055579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.335 × 10⁹⁰(91-digit number)

63354753674597543158…66473815174814055581

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

1.267 × 10⁹¹(92-digit number)

12670950734919508631…32947630349628111159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.267 × 10⁹¹(92-digit number)

12670950734919508631…32947630349628111161

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

2.534 × 10⁹¹(92-digit number)

25341901469839017263…65895260699256222319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.534 × 10⁹¹(92-digit number)

25341901469839017263…65895260699256222321

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

5.068 × 10⁹¹(92-digit number)

50683802939678034526…31790521398512444639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.068 × 10⁹¹(92-digit number)

50683802939678034526…31790521398512444641

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