Block #161,634

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/12/2013, 7:17:05 PM · Difficulty 9.8597 · 6,640,936 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

004755578c08ec6a1d88ad5cbac5e48fd02f62707b707327cc5f8c97a5ead683

View on Chainz ↗

Height

#161,634

Difficulty

9.859651

Transactions

Size

733 B

Version

Bits

09dc1212

Nonce

337,108

Timestamp

9/12/2013, 7:17:05 PM

Confirmations

6,640,936

Mined by

⛏️ P2SHAKhaGKFX4s17sd56QzVFtsa8mSKjeAXtBv

Merkle Root

9a8cc64b2e5965eda02daca1fe0b23f32c37d1541b90af5ce8a7def9450ce17f

Transactions (2)

Coinbase6522c545786e0f…9e38087ef211a7

1 in → 1 out10.2800 XPM109 B

AKhaGKFX…KjeAXtBv

1583459e25b93b…34385d9da39109

4 in → 2 out41.1200 XPM535 B

AWTcHbXr…6Y9QWARW AFz9fXym…wh4UqpkL

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.

1.953 × 10⁹¹(92-digit number)

19537411809053300858…05688637246404997919

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

1.953 × 10⁹¹(92-digit number)

19537411809053300858…05688637246404997919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.953 × 10⁹¹(92-digit number)

19537411809053300858…05688637246404997921

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

3.907 × 10⁹¹(92-digit number)

39074823618106601716…11377274492809995839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.907 × 10⁹¹(92-digit number)

39074823618106601716…11377274492809995841

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

7.814 × 10⁹¹(92-digit number)

78149647236213203433…22754548985619991679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.814 × 10⁹¹(92-digit number)

78149647236213203433…22754548985619991681

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

1.562 × 10⁹²(93-digit number)

15629929447242640686…45509097971239983359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.562 × 10⁹²(93-digit number)

15629929447242640686…45509097971239983361

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

3.125 × 10⁹²(93-digit number)

31259858894485281373…91018195942479966719

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