Block #214,906

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 6:28:56 PM · Difficulty 9.9244 · 6,581,973 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3c6cd7a9df11e8e9ab4fef9c9978437a58175814df7ff95c829b4fbc445ff71

View on Chainz ↗

Height

#214,906

Difficulty

9.924442

Transactions

Size

5.26 KB

Version

Bits

09eca83e

Nonce

1,165,138,569

Timestamp

10/17/2013, 6:28:56 PM

Confirmations

6,581,973

Mined by

⛏️ zGR`,ANyfRGM7iwYc5JMPbu4aDF1bK1dZDmhtRa

Merkle Root

b2f77e0589500e0e0a34a7cf4706fc60eca09d9267a843b69169c905e9093458

Transactions (1)

Coinbaseb2f77e0589500e…69c905e9093458

1 in → 154 out10.0800 XPM5.17 KB

ANyfRGM7…dZDmhtRa AeU72TuE…Kopwd476 ASGXhVnp…gHNxHQYB AXKZFkpB…7jq391N4 ATwXrZXP…rirMzEJV

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.

4.019 × 10⁹¹(92-digit number)

40199983539427187348…10867970032642711999

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

4.019 × 10⁹¹(92-digit number)

40199983539427187348…10867970032642711999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.019 × 10⁹¹(92-digit number)

40199983539427187348…10867970032642712001

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

8.039 × 10⁹¹(92-digit number)

80399967078854374697…21735940065285423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.039 × 10⁹¹(92-digit number)

80399967078854374697…21735940065285424001

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

1.607 × 10⁹²(93-digit number)

16079993415770874939…43471880130570847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.607 × 10⁹²(93-digit number)

16079993415770874939…43471880130570848001

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

3.215 × 10⁹²(93-digit number)

32159986831541749879…86943760261141695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.215 × 10⁹²(93-digit number)

32159986831541749879…86943760261141696001

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

6.431 × 10⁹²(93-digit number)

64319973663083499758…73887520522283391999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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