Block #331,380

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 8:18:43 AM · Difficulty 10.1661 · 6,483,085 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee76eeea8b272b7c3e5e8d72204159fa729e8291e08f762ff035feba0cf5d91b

View on Chainz ↗

Height

#331,380

Difficulty

10.166054

Transactions

Size

208 B

Version

Bits

0a2a828c

Nonce

1,908

Timestamp

12/27/2013, 8:18:43 AM

Confirmations

6,483,085

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f4874b8605aedc63dc73bd21831163908dc99355fd16bf7bed85a693d738db37

Transactions (1)

Coinbasef4874b8605aedc…85a693d738db37

1 in → 1 out9.6600 XPM116 B

AbwWkWZt…kawDhufa

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.

2.176 × 10¹⁰⁰(101-digit number)

21766476179206919283…82570591983483084799

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

2.176 × 10¹⁰⁰(101-digit number)

21766476179206919283…82570591983483084799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.176 × 10¹⁰⁰(101-digit number)

21766476179206919283…82570591983483084801

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

4.353 × 10¹⁰⁰(101-digit number)

43532952358413838566…65141183966966169599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.353 × 10¹⁰⁰(101-digit number)

43532952358413838566…65141183966966169601

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

8.706 × 10¹⁰⁰(101-digit number)

87065904716827677133…30282367933932339199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.706 × 10¹⁰⁰(101-digit number)

87065904716827677133…30282367933932339201

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

1.741 × 10¹⁰¹(102-digit number)

17413180943365535426…60564735867864678399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.741 × 10¹⁰¹(102-digit number)

17413180943365535426…60564735867864678401

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

3.482 × 10¹⁰¹(102-digit number)

34826361886731070853…21129471735729356799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.482 × 10¹⁰¹(102-digit number)

34826361886731070853…21129471735729356801

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 #331,380

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