Block #11,345

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 6:18:46 AM · Difficulty 7.7149 · 6,778,142 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be31139ee288e89781eb6e95460811550cf8c6840588252e06984a78f0e345af

View on Chainz ↗

Height

#11,345

Difficulty

7.714854

Transactions

Size

198 B

Version

Bits

07b700a4

Nonce

Timestamp

7/11/2013, 6:18:46 AM

Confirmations

6,778,142

Merkle Root

f01e025f6ae71f0764d436273cdbbdc819506b31e21e930a090c2b44b1e96249

Transactions (1)

Coinbasef01e025f6ae71f…0c2b44b1e96249

1 in → 1 out16.7800 XPM109 B

AGY4TBx7…YfD8h7Va

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.

7.213 × 10⁹²(93-digit number)

72134694238831380554…84279684893976373799

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

7.213 × 10⁹²(93-digit number)

72134694238831380554…84279684893976373799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.213 × 10⁹²(93-digit number)

72134694238831380554…84279684893976373801

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

1.442 × 10⁹³(94-digit number)

14426938847766276110…68559369787952747599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.442 × 10⁹³(94-digit number)

14426938847766276110…68559369787952747601

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

2.885 × 10⁹³(94-digit number)

28853877695532552221…37118739575905495199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.885 × 10⁹³(94-digit number)

28853877695532552221…37118739575905495201

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

5.770 × 10⁹³(94-digit number)

57707755391065104443…74237479151810990399

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