Block #327,347

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 11:59:52 AM · Difficulty 10.1760 · 6,482,113 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4a4e9d394e719667f5c17b35a43c81bce61f763c0d2faa14751fdaa47519490

View on Chainz ↗

Height

#327,347

Difficulty

10.175987

Transactions

Size

1.01 KB

Version

Bits

0a2d0d7d

Nonce

119,838

Timestamp

12/24/2013, 11:59:52 AM

Confirmations

6,482,113

Mined by

⛏️ aRvAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

96711bf8e0240155dc39f324c79b194bce4dfb978f449cfd54ca80bbb9153631

Transactions (1)

Coinbase96711bf8e02401…ca80bbb9153631

1 in → 26 out9.6400 XPM947 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AHXE2yX3…eKeKBMdK AeFawUfC…dps5LLeM

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.

2.902 × 10⁹⁷(98-digit number)

29025541050814761989…49553888991068371199

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

2.902 × 10⁹⁷(98-digit number)

29025541050814761989…49553888991068371199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.902 × 10⁹⁷(98-digit number)

29025541050814761989…49553888991068371201

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

5.805 × 10⁹⁷(98-digit number)

58051082101629523978…99107777982136742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.805 × 10⁹⁷(98-digit number)

58051082101629523978…99107777982136742401

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

1.161 × 10⁹⁸(99-digit number)

11610216420325904795…98215555964273484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.161 × 10⁹⁸(99-digit number)

11610216420325904795…98215555964273484801

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

2.322 × 10⁹⁸(99-digit number)

23220432840651809591…96431111928546969599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.322 × 10⁹⁸(99-digit number)

23220432840651809591…96431111928546969601

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

4.644 × 10⁹⁸(99-digit number)

46440865681303619183…92862223857093939199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.644 × 10⁹⁸(99-digit number)

46440865681303619183…92862223857093939201

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

Block #327,347

Cookie Preferences