Block #337,138

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 11:04:48 AM · Difficulty 10.1406 · 6,458,550 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e0348f50cdd0d07c84451c36e5aa2c73ec7451374f7e9f9bb4d71796d108135

View on Chainz ↗

Height

#337,138

Difficulty

10.140648

Transactions

Size

427 B

Version

Bits

0a240189

Nonce

377,534

Timestamp

12/31/2013, 11:04:48 AM

Confirmations

6,458,550

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7e57fb1607b5fa02e61bb7c279ea70a280d05881bc3c8467d56acb208f20a225

Transactions (2)

Coinbasebaaf653b130015…04475051f9a681

1 in → 1 out9.7200 XPM110 B

AeKNrjNj…1NEq95Ta

96b551b8959782…cbf6ea82fea154

1 in → 2 out199.9900 XPM226 B

AXts237W…xzdtnyAB AVyuHXCy…Gc1KSpKq

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.

3.394 × 10⁹⁶(97-digit number)

33940170356073015455…59699033278399286399

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

3.394 × 10⁹⁶(97-digit number)

33940170356073015455…59699033278399286399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.394 × 10⁹⁶(97-digit number)

33940170356073015455…59699033278399286401

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

6.788 × 10⁹⁶(97-digit number)

67880340712146030911…19398066556798572799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.788 × 10⁹⁶(97-digit number)

67880340712146030911…19398066556798572801

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

1.357 × 10⁹⁷(98-digit number)

13576068142429206182…38796133113597145599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.357 × 10⁹⁷(98-digit number)

13576068142429206182…38796133113597145601

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

2.715 × 10⁹⁷(98-digit number)

27152136284858412364…77592266227194291199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.715 × 10⁹⁷(98-digit number)

27152136284858412364…77592266227194291201

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

5.430 × 10⁹⁷(98-digit number)

54304272569716824729…55184532454388582399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.430 × 10⁹⁷(98-digit number)

54304272569716824729…55184532454388582401

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