Block #324,156

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2013, 3:17:11 AM · Difficulty 10.2092 · 6,490,011 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a82470c0a7ed88c815cd30d2b204081f0d04638e825eacf7382e370bef7e0c96

View on Chainz ↗

Height

#324,156

Difficulty

10.209192

Transactions

Size

1.08 KB

Version

Bits

0a358d9e

Nonce

31,343

Timestamp

12/22/2013, 3:17:11 AM

Confirmations

6,490,011

Mined by

⛏️ <aRYBAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

19288ad69bfabcb9882a8e2ed112b23059aab4bf0661098a92a82f6d4bca4ba5

Transactions (1)

Coinbase19288ad69bfabc…a82f6d4bca4ba5

1 in → 28 out9.5600 XPM1015 B

Ad9pSzHt…cpJ3y2zz AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AP7nJS9V…Lay59hK5

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.

4.725 × 10⁹⁷(98-digit number)

47252824742043882406…60580789634029434799

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

4.725 × 10⁹⁷(98-digit number)

47252824742043882406…60580789634029434799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.725 × 10⁹⁷(98-digit number)

47252824742043882406…60580789634029434801

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

9.450 × 10⁹⁷(98-digit number)

94505649484087764813…21161579268058869599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.450 × 10⁹⁷(98-digit number)

94505649484087764813…21161579268058869601

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

1.890 × 10⁹⁸(99-digit number)

18901129896817552962…42323158536117739199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.890 × 10⁹⁸(99-digit number)

18901129896817552962…42323158536117739201

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

3.780 × 10⁹⁸(99-digit number)

37802259793635105925…84646317072235478399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.780 × 10⁹⁸(99-digit number)

37802259793635105925…84646317072235478401

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

7.560 × 10⁹⁸(99-digit number)

75604519587270211851…69292634144470956799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.560 × 10⁹⁸(99-digit number)

75604519587270211851…69292634144470956801

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

Block #324,156

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