Block #332,318

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 11:12:05 PM · Difficulty 10.1744 · 6,473,026 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b323658cfbaeda25021a03ca51151307491ba4260ec3c611f2ee82481890613

View on Chainz ↗

Height

#332,318

Difficulty

10.174437

Transactions

Size

429 B

Version

Bits

0a2ca7e3

Nonce

385,819

Timestamp

12/27/2013, 11:12:05 PM

Confirmations

6,473,026

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

29d9cbd0902896c12fdfd2ea7a438b2c3af72f0e9233379d1296515c0e617d69

Transactions (2)

Coinbase11ba4644de72b8…33b605a4ba73ba

1 in → 1 out9.6600 XPM110 B

AeKNrjNj…1NEq95Ta

d570e9c6fb2a14…0e9f78e313597a

1 in → 2 out4.0248 XPM225 B

AFx3SfER…eT5gZyj6 AMu4YTFf…SwFhX9P2

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.

1.507 × 10¹⁰³(104-digit number)

15079717780415738346…32466183037875100659

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

1.507 × 10¹⁰³(104-digit number)

15079717780415738346…32466183037875100659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.507 × 10¹⁰³(104-digit number)

15079717780415738346…32466183037875100661

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

3.015 × 10¹⁰³(104-digit number)

30159435560831476693…64932366075750201319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.015 × 10¹⁰³(104-digit number)

30159435560831476693…64932366075750201321

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

6.031 × 10¹⁰³(104-digit number)

60318871121662953387…29864732151500402639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.031 × 10¹⁰³(104-digit number)

60318871121662953387…29864732151500402641

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

1.206 × 10¹⁰⁴(105-digit number)

12063774224332590677…59729464303000805279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.206 × 10¹⁰⁴(105-digit number)

12063774224332590677…59729464303000805281

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

2.412 × 10¹⁰⁴(105-digit number)

24127548448665181354…19458928606001610559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.412 × 10¹⁰⁴(105-digit number)

24127548448665181354…19458928606001610561

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