Block #263,341

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/17/2013, 5:25:16 PM · Difficulty 9.9665 · 6,539,191 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

69dfe8becd283bccec10c7555b290d40c175bf0cba340bb652a1e4abaff906ed

View on Chainz ↗

Height

#263,341

Difficulty

9.966478

Transactions

Size

979 B

Version

Bits

09f76b13

Nonce

39,352

Timestamp

11/17/2013, 5:25:16 PM

Confirmations

6,539,191

Mined by

⛏️ P2SHAMV6YmkAX84bza6mMS1EA8taZU9TvN6hA8

Merkle Root

10e3997cdf0547bd3c9041c3820fad86dd981a37a08176b5060d7f63e6da9a3e

Transactions (3)

Coinbase4fcc7ebb1d9bb3…8bf8c4c3abd3f7

1 in → 1 out10.0700 XPM109 B

AMV6YmkA…9TvN6hA8

824e232c3066e5…19bb010c0d801a

3 in → 2 out800.0100 XPM521 B

AVHE9gPz…c9Uzu8ia ASzB7F59…9VwK4HYR

fa0a6a48e9b68b…2d65cdcc689844

1 in → 4 out10.0200 XPM260 B

ASNYeTKF…CRfjh97X AeKNrjNj…1NEq95Ta AREyVUQx…fNuPnjDA AUfa5LFJ…C4BhhWGa

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.

1.595 × 10⁹¹(92-digit number)

15950771806469340715…57597830717970073599

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

1.595 × 10⁹¹(92-digit number)

15950771806469340715…57597830717970073599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.595 × 10⁹¹(92-digit number)

15950771806469340715…57597830717970073601

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

3.190 × 10⁹¹(92-digit number)

31901543612938681430…15195661435940147199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.190 × 10⁹¹(92-digit number)

31901543612938681430…15195661435940147201

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

6.380 × 10⁹¹(92-digit number)

63803087225877362860…30391322871880294399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.380 × 10⁹¹(92-digit number)

63803087225877362860…30391322871880294401

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

1.276 × 10⁹²(93-digit number)

12760617445175472572…60782645743760588799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.276 × 10⁹²(93-digit number)

12760617445175472572…60782645743760588801

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

2.552 × 10⁹²(93-digit number)

25521234890350945144…21565291487521177599

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