Block #321,268

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/20/2013, 5:12:36 AM · Difficulty 10.1889 · 6,471,269 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab4cf863c846fe10345b97fe6d699953c2ad2a049d39a5e1aa2285e3a426a495

View on Chainz ↗

Height

#321,268

Difficulty

10.188930

Transactions

Size

1.08 KB

Version

Bits

0a305db6

Nonce

59,295

Timestamp

12/20/2013, 5:12:36 AM

Confirmations

6,471,269

Merkle Root

780babef8e53b61255517b9f57bb053db4d0aef8612e40b944d510c1a6f01e87

Transactions (1)

Coinbase780babef8e53b6…d510c1a6f01e87

1 in → 28 out9.6000 XPM1015 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1 AXmS7tZu…11YypHLP

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.

2.292 × 10⁹⁶(97-digit number)

22921867637134722318…04942596313365643519

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

2.292 × 10⁹⁶(97-digit number)

22921867637134722318…04942596313365643519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.292 × 10⁹⁶(97-digit number)

22921867637134722318…04942596313365643521

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

4.584 × 10⁹⁶(97-digit number)

45843735274269444637…09885192626731287039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.584 × 10⁹⁶(97-digit number)

45843735274269444637…09885192626731287041

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

9.168 × 10⁹⁶(97-digit number)

91687470548538889274…19770385253462574079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.168 × 10⁹⁶(97-digit number)

91687470548538889274…19770385253462574081

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

1.833 × 10⁹⁷(98-digit number)

18337494109707777854…39540770506925148159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.833 × 10⁹⁷(98-digit number)

18337494109707777854…39540770506925148161

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

3.667 × 10⁹⁷(98-digit number)

36674988219415555709…79081541013850296319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.667 × 10⁹⁷(98-digit number)

36674988219415555709…79081541013850296321

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