Block #11,340

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 6:17:27 AM · Difficulty 7.7147 · 6,778,214 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cccb8828c3fc0828186972234ca034be3f551ce1d01532e6bc9424f0c3713f96

View on Chainz ↗

Height

#11,340

Difficulty

7.714661

Transactions

Size

202 B

Version

Bits

07b6f405

Nonce

125

Timestamp

7/11/2013, 6:17:27 AM

Confirmations

6,778,214

Merkle Root

c0859e7f5a3c4cad56a06ce9a584247d3fae3e1416e05d3084809e3d8489cd20

Transactions (1)

Coinbasec0859e7f5a3c4c…809e3d8489cd20

1 in → 1 out16.7800 XPM108 B

AaadRFdu…KzYHzbJN

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.

1.666 × 10¹⁰³(104-digit number)

16667494844921557183…89935876658880995359

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

1.666 × 10¹⁰³(104-digit number)

16667494844921557183…89935876658880995359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.666 × 10¹⁰³(104-digit number)

16667494844921557183…89935876658880995361

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

3.333 × 10¹⁰³(104-digit number)

33334989689843114367…79871753317761990719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.333 × 10¹⁰³(104-digit number)

33334989689843114367…79871753317761990721

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

6.666 × 10¹⁰³(104-digit number)

66669979379686228735…59743506635523981439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.666 × 10¹⁰³(104-digit number)

66669979379686228735…59743506635523981441

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

1.333 × 10¹⁰⁴(105-digit number)

13333995875937245747…19487013271047962879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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

CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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