Block #271,685

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 6:57:58 PM · Difficulty 9.9522 · 6,524,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

090e76e37867a5b83de3595773c4bc476301029277374eceb1c4f9052b8aa1e6

View on Chainz ↗

Height

#271,685

Difficulty

9.952215

Transactions

Size

1.72 KB

Version

Bits

09f3c465

Nonce

135,067

Timestamp

11/24/2013, 6:57:58 PM

Confirmations

6,524,426

Mined by

⛏️ E%aRLAVzhvfTX6hcvuz5akKkM7Fnv6uZzNJYq61

Merkle Root

3613123f85691ce8af1dfa507b77c98161f37240bcd724dbc4fbb6abdb1be0ef

Transactions (4)

Coinbaseb2ee958dcbbbdd…6527cdfedac107

1 in → 25 out10.0800 XPM913 B

AVzhvfTX…ZzNJYq61 AUSGA5VC…GYHbnJtz AUsdND2U…PxHWEPmG AGPBDvpY…HsUDJ9oq ALdHh27b…XNbqrvPf

a45d78c8bf8f74…fc9a8690dc38c1

2 in → 2 out49.8107 XPM376 B

AQUC7Hue…LL2XMoNY AWf6M2Ts…S4FeiozU

811426536a5dd5…57787b3b5bf19b

1 in → 1 out10.0500 XPM158 B

ATHyDZ4z…zbc38ysp

7cd3a549420f0f…b1e7c97a1e9c85

1 in → 2 out9.0245 XPM225 B

AGTtcepQ…V6LF5d19 AQfLLdUM…y696muyi

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.

2.157 × 10⁹⁸(99-digit number)

21570826126313322859…20637149544808078079

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

2.157 × 10⁹⁸(99-digit number)

21570826126313322859…20637149544808078079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.157 × 10⁹⁸(99-digit number)

21570826126313322859…20637149544808078081

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

4.314 × 10⁹⁸(99-digit number)

43141652252626645719…41274299089616156159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.314 × 10⁹⁸(99-digit number)

43141652252626645719…41274299089616156161

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

8.628 × 10⁹⁸(99-digit number)

86283304505253291438…82548598179232312319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.628 × 10⁹⁸(99-digit number)

86283304505253291438…82548598179232312321

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

1.725 × 10⁹⁹(100-digit number)

17256660901050658287…65097196358464624639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.725 × 10⁹⁹(100-digit number)

17256660901050658287…65097196358464624641

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

3.451 × 10⁹⁹(100-digit number)

34513321802101316575…30194392716929249279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.451 × 10⁹⁹(100-digit number)

34513321802101316575…30194392716929249281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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