Block #330,878

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/26/2013, 11:47:50 PM · Difficulty 10.1675 · 6,463,475 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a433821f937112d76b632606216febd30f830f751afdf21dd2c6c0e9bce5173e

View on Chainz ↗

Height

#330,878

Difficulty

10.167492

Transactions

Size

1.09 KB

Version

Bits

0a2ae0c5

Nonce

10,125

Timestamp

12/26/2013, 11:47:50 PM

Confirmations

6,463,475

Merkle Root

2a6691929a5fa902a36b8ced92f51ae3d3dd36b7442bbc9f8f8e6ec00a8429f6

Transactions (4)

Coinbase4655605ff6e908…e7e06df7efb27d

1 in → 1 out9.6600 XPM97 B

AYCeLhqB…eqGM6KK1

ce747f2d4457e3…a9c73b2986a196

2 in → 7 out19.2800 XPM477 B

AeKNrjNj…1NEq95Ta AcR9znqK…xePBi7CS AZHEpaqf…MxbjTDc5 AXy1QDP5…39wz5ZVg AdkZ3hkz…JCYhZRGU

5028f2c23826e8…c148562ecc51c6

1 in → 2 out219.9600 XPM225 B

AVvyhacf…VgfUiyaR AU35XgRL…EYF4xXtQ

4d12dcc0a0fc34…8d8a633f079cb4

1 in → 2 out6.5648 XPM225 B

AeXEE9bU…K7M3huKw Aa7gkVRn…29a9rMC4

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.

1.728 × 10⁹⁹(100-digit number)

17281077412787263692…40866457620762844799

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

1.728 × 10⁹⁹(100-digit number)

17281077412787263692…40866457620762844799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.728 × 10⁹⁹(100-digit number)

17281077412787263692…40866457620762844801

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

3.456 × 10⁹⁹(100-digit number)

34562154825574527384…81732915241525689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.456 × 10⁹⁹(100-digit number)

34562154825574527384…81732915241525689601

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

6.912 × 10⁹⁹(100-digit number)

69124309651149054769…63465830483051379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.912 × 10⁹⁹(100-digit number)

69124309651149054769…63465830483051379201

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

1.382 × 10¹⁰⁰(101-digit number)

13824861930229810953…26931660966102758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.382 × 10¹⁰⁰(101-digit number)

13824861930229810953…26931660966102758401

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

2.764 × 10¹⁰⁰(101-digit number)

27649723860459621907…53863321932205516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.764 × 10¹⁰⁰(101-digit number)

27649723860459621907…53863321932205516801

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