Block #272,351

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 5:24:02 AM · Difficulty 9.9526 · 6,520,648 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4c5588cce2e88c24b9057740aabe369e89c01fd4c29d7ba12a40ec7210486c9

View on Chainz ↗

Height

#272,351

Difficulty

9.952589

Transactions

Size

198 B

Version

Bits

09f3dcdc

Nonce

34,221

Timestamp

11/25/2013, 5:24:02 AM

Confirmations

6,520,648

Merkle Root

03b4c68a69ef7f9d693c2b9d165df64709b7b44ecbb066a6029dd907e4657e2e

Transactions (1)

Coinbase03b4c68a69ef7f…9dd907e4657e2e

1 in → 1 out10.0800 XPM109 B

AZTX6qTp…pRvdLPFU

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.

8.146 × 10⁹¹(92-digit number)

81469258942930183989…20179279742400128699

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

8.146 × 10⁹¹(92-digit number)

81469258942930183989…20179279742400128699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.146 × 10⁹¹(92-digit number)

81469258942930183989…20179279742400128701

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

1.629 × 10⁹²(93-digit number)

16293851788586036797…40358559484800257399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.629 × 10⁹²(93-digit number)

16293851788586036797…40358559484800257401

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

3.258 × 10⁹²(93-digit number)

32587703577172073595…80717118969600514799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.258 × 10⁹²(93-digit number)

32587703577172073595…80717118969600514801

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

6.517 × 10⁹²(93-digit number)

65175407154344147191…61434237939201029599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.517 × 10⁹²(93-digit number)

65175407154344147191…61434237939201029601

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

1.303 × 10⁹³(94-digit number)

13035081430868829438…22868475878402059199

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