Block #192,687

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 1:11:24 AM · Difficulty 9.8747 · 6,612,673 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d49fc2aa503944082c48ed6a38449bbc849b0a18fe27595676c5c7ce3008afd8

View on Chainz ↗

Height

#192,687

Difficulty

9.874681

Transactions

Size

3.97 KB

Version

Bits

09dfeb13

Nonce

1,165,029,343

Timestamp

10/4/2013, 1:11:24 AM

Confirmations

6,612,673

Mined by

⛏️ RNIAWWaDRnPF3uYSRjvC9Pw8et1mLqR1zB7PV

Merkle Root

c899d0701182c53e53ee6dd7b1b6e1eb89a1373090619e51a6ba67922aac3589

Transactions (1)

Coinbasec899d0701182c5…ba67922aac3589

1 in → 115 out10.2000 XPM3.88 KB

AWWaDRnP…qR1zB7PV AS5X2XNw…NKGEK3GT AeLXg8qu…77XGoqwh AQTQxLiv…s1fK2esi ANxERLYc…v7fC1vqc

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.

3.126 × 10⁹⁷(98-digit number)

31260911236086069319…73542748684881248799

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

3.126 × 10⁹⁷(98-digit number)

31260911236086069319…73542748684881248799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.126 × 10⁹⁷(98-digit number)

31260911236086069319…73542748684881248801

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

6.252 × 10⁹⁷(98-digit number)

62521822472172138638…47085497369762497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.252 × 10⁹⁷(98-digit number)

62521822472172138638…47085497369762497601

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

1.250 × 10⁹⁸(99-digit number)

12504364494434427727…94170994739524995199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.250 × 10⁹⁸(99-digit number)

12504364494434427727…94170994739524995201

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

2.500 × 10⁹⁸(99-digit number)

25008728988868855455…88341989479049990399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.500 × 10⁹⁸(99-digit number)

25008728988868855455…88341989479049990401

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

5.001 × 10⁹⁸(99-digit number)

50017457977737710910…76683978958099980799

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