Block #182,372

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/27/2013, 6:17:13 AM · Difficulty 9.8587 · 6,628,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c47a67aa8a8621f321fd59bd1070295761edb2ee1692c3bb5896fa575d9a9fd

View on Chainz ↗

Height

#182,372

Difficulty

9.858665

Transactions

Size

574 B

Version

Bits

09dbd172

Nonce

25,777

Timestamp

9/27/2013, 6:17:13 AM

Confirmations

6,628,580

Mined by

⛏️ P2SHAYc3QGYaSv1sA3FuuZuBoiE4ttSWDuszQp

Merkle Root

80a5547e0b8fa1d433c90eff2b0b6887eab4a71681a940badab69369d6ceae8c

Transactions (2)

Coinbasea627f8d9d90872…65cac161269a0d

1 in → 1 out10.2800 XPM109 B

AYc3QGYa…SWDuszQp

e354066c2d78ff…a0aa36d7f12160

2 in → 2 out15.4792 XPM375 B

AQUzNJxr…Y543YsZB ATzXUYiy…2MtWrZ1g

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.

5.040 × 10⁹⁴(95-digit number)

50402694707572607202…79393019258034464639

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

5.040 × 10⁹⁴(95-digit number)

50402694707572607202…79393019258034464639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.040 × 10⁹⁴(95-digit number)

50402694707572607202…79393019258034464641

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

1.008 × 10⁹⁵(96-digit number)

10080538941514521440…58786038516068929279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.008 × 10⁹⁵(96-digit number)

10080538941514521440…58786038516068929281

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

2.016 × 10⁹⁵(96-digit number)

20161077883029042880…17572077032137858559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.016 × 10⁹⁵(96-digit number)

20161077883029042880…17572077032137858561

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

4.032 × 10⁹⁵(96-digit number)

40322155766058085761…35144154064275717119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.032 × 10⁹⁵(96-digit number)

40322155766058085761…35144154064275717121

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

8.064 × 10⁹⁵(96-digit number)

80644311532116171523…70288308128551434239

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

Block #182,372

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