Block #30,462

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 7:14:46 PM · Difficulty 7.9869 · 6,783,894 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3c36a848d0fa4f15f3c983d6fc8183cc5744db5534cf0c3cb7077629af367d4

View on Chainz ↗

Height

#30,462

Difficulty

7.986911

Transactions

Size

205 B

Version

Bits

07fca62e

Nonce

289

Timestamp

7/13/2013, 7:14:46 PM

Confirmations

6,783,894

Mined by

⛏️ P2SHALXjrugCYbt29xU2ER2ywowb9GhByoynjy

Merkle Root

4c35397824aca56e0f9f1da22e06f8327025be78eadbe23596fc31d2b5cef70e

Transactions (1)

Coinbase4c35397824aca5…fc31d2b5cef70e

1 in → 1 out15.6600 XPM108 B

ALXjrugC…hByoynjy

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.

1.779 × 10¹¹¹(112-digit number)

17794446524133891595…14562882234393546999

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

1.779 × 10¹¹¹(112-digit number)

17794446524133891595…14562882234393546999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.779 × 10¹¹¹(112-digit number)

17794446524133891595…14562882234393547001

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

3.558 × 10¹¹¹(112-digit number)

35588893048267783190…29125764468787093999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.558 × 10¹¹¹(112-digit number)

35588893048267783190…29125764468787094001

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

7.117 × 10¹¹¹(112-digit number)

71177786096535566381…58251528937574187999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.117 × 10¹¹¹(112-digit number)

71177786096535566381…58251528937574188001

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

1.423 × 10¹¹²(113-digit number)

14235557219307113276…16503057875148375999

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

Block #30,462

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