Block #82,339

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 8:50:21 AM · Difficulty 9.2745 · 6,721,408 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a642bfcb5562ebf4b9af02a5efa2d5627e5b8d5fe1e172bf9a8ef7b0599f218

View on Chainz ↗

Height

#82,339

Difficulty

9.274524

Transactions

Size

1.02 KB

Version

Bits

0946472d

Nonce

1,701

Timestamp

7/25/2013, 8:50:21 AM

Confirmations

6,721,408

Mined by

⛏️ P2SHARHgBzaNyGwKtxNyetDjaovMQmaVqBMbqG

Merkle Root

a18f0f6e0275a195e9ec56e45c29af318a79c7a7ca2750bd529943394bea139c

Transactions (3)

Coinbasec388c93ff10a60…a3b4ab5059de56

1 in → 1 out11.6300 XPM110 B

ARHgBzaN…aVqBMbqG

41c16084e5eb52…a56329da54189f

5 in → 1 out78.6800 XPM616 B

APhBYPx5…qvP6hNmQ

28cf631b8e8cb5…bc2ab53c8b1111

1 in → 2 out1.1900 XPM227 B

AeubMQ8E…gVupRs7G AGC2uj9h…SgzXHvcE

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.

6.154 × 10⁹⁹(100-digit number)

61543273571700698883…69155674717882660169

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

6.154 × 10⁹⁹(100-digit number)

61543273571700698883…69155674717882660169

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.154 × 10⁹⁹(100-digit number)

61543273571700698883…69155674717882660171

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

1.230 × 10¹⁰⁰(101-digit number)

12308654714340139776…38311349435765320339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.230 × 10¹⁰⁰(101-digit number)

12308654714340139776…38311349435765320341

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

2.461 × 10¹⁰⁰(101-digit number)

24617309428680279553…76622698871530640679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.461 × 10¹⁰⁰(101-digit number)

24617309428680279553…76622698871530640681

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

4.923 × 10¹⁰⁰(101-digit number)

49234618857360559107…53245397743061281359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.923 × 10¹⁰⁰(101-digit number)

49234618857360559107…53245397743061281361

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

9.846 × 10¹⁰⁰(101-digit number)

98469237714721118214…06490795486122562719

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