Block #323,796

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 9:30:03 PM · Difficulty 10.2072 · 6,493,533 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aad4a598441666a34c6b54dac1ae18c6258a926d1abee945e1cd437e51178f5f

View on Chainz ↗

Height

#323,796

Difficulty

10.207212

Transactions

Size

1.05 KB

Version

Bits

0a350bd6

Nonce

90,855

Timestamp

12/21/2013, 9:30:03 PM

Confirmations

6,493,533

Mined by

⛏️ aRZAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

d61f75e7cb352087a0e27b6011088ec254de8f63e4fc85c35dc71530690a8f7d

Transactions (1)

Coinbased61f75e7cb3520…c71530690a8f7d

1 in → 27 out9.5800 XPM981 B

Aac9Hjdg…P4ktypc3 APeshfYV…3PKcKMKH AG5YAjec…VhA4Aeh1 AYtDvcGs…VuAcA7m7 AZ2pPuKg…95SN2Yr7

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.

4.639 × 10⁹³(94-digit number)

46398663043480854770…19424443333915993599

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

4.639 × 10⁹³(94-digit number)

46398663043480854770…19424443333915993599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.639 × 10⁹³(94-digit number)

46398663043480854770…19424443333915993601

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

9.279 × 10⁹³(94-digit number)

92797326086961709541…38848886667831987199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.279 × 10⁹³(94-digit number)

92797326086961709541…38848886667831987201

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

1.855 × 10⁹⁴(95-digit number)

18559465217392341908…77697773335663974399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.855 × 10⁹⁴(95-digit number)

18559465217392341908…77697773335663974401

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

3.711 × 10⁹⁴(95-digit number)

37118930434784683816…55395546671327948799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.711 × 10⁹⁴(95-digit number)

37118930434784683816…55395546671327948801

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

7.423 × 10⁹⁴(95-digit number)

74237860869569367633…10791093342655897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.423 × 10⁹⁴(95-digit number)

74237860869569367633…10791093342655897601

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 #323,796

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