Block #326,274

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/23/2013, 4:23:13 PM · Difficulty 10.1924 · 6,481,333 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5fa2f381303a287e7422a79d8222fecf08d06346b7aca628f69ca79b941e02d9

View on Chainz ↗

Height

#326,274

Difficulty

10.192375

Transactions

Size

971 B

Version

Bits

0a313f75

Nonce

94,265

Timestamp

12/23/2013, 4:23:13 PM

Confirmations

6,481,333

Mined by

⛏️ aRcAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

fd4c1ff9019d35b8960629a2d0590b37f099570c3c2a1ff8b28165d849473686

Transactions (1)

Coinbasefd4c1ff9019d35…8165d849473686

1 in → 24 out9.6100 XPM879 B

AQwRN8bE…V8PsTcY9 AG5YAjec…VhA4Aeh1 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz

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.

1.736 × 10⁹⁹(100-digit number)

17360404371044080153…94345919074377151599

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

1.736 × 10⁹⁹(100-digit number)

17360404371044080153…94345919074377151599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.736 × 10⁹⁹(100-digit number)

17360404371044080153…94345919074377151601

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

3.472 × 10⁹⁹(100-digit number)

34720808742088160307…88691838148754303199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.472 × 10⁹⁹(100-digit number)

34720808742088160307…88691838148754303201

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

6.944 × 10⁹⁹(100-digit number)

69441617484176320614…77383676297508606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.944 × 10⁹⁹(100-digit number)

69441617484176320614…77383676297508606401

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

1.388 × 10¹⁰⁰(101-digit number)

13888323496835264122…54767352595017212799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.388 × 10¹⁰⁰(101-digit number)

13888323496835264122…54767352595017212801

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

2.777 × 10¹⁰⁰(101-digit number)

27776646993670528245…09534705190034425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.777 × 10¹⁰⁰(101-digit number)

27776646993670528245…09534705190034425601

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 #326,274

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