Block #323,651

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/21/2013, 7:06:10 PM · Difficulty 10.2070 · 6,471,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cd78a463ae514d718bea19d47d3abde8cb0e2f88c4c4d280151f997a4c5b4b0

View on Chainz ↗

Height

#323,651

Difficulty

10.206973

Transactions

Size

1.08 KB

Version

Bits

0a34fc2c

Nonce

8,037

Timestamp

12/21/2013, 7:06:10 PM

Confirmations

6,471,366

Mined by

⛏️ CaRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

934c0de70e6b8e0b476eb568d7588de515933b3052578979ace00c09befb5cf7

Transactions (1)

Coinbase934c0de70e6b8e…e00c09befb5cf7

1 in → 28 out9.5600 XPM1015 B

Ad9pSzHt…cpJ3y2zz AQwRN8bE…V8PsTcY9 AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR

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.

3.292 × 10¹⁰⁰(101-digit number)

32920969544080728912…53966588172143600639

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

3.292 × 10¹⁰⁰(101-digit number)

32920969544080728912…53966588172143600639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.292 × 10¹⁰⁰(101-digit number)

32920969544080728912…53966588172143600641

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

6.584 × 10¹⁰⁰(101-digit number)

65841939088161457824…07933176344287201279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.584 × 10¹⁰⁰(101-digit number)

65841939088161457824…07933176344287201281

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

1.316 × 10¹⁰¹(102-digit number)

13168387817632291564…15866352688574402559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.316 × 10¹⁰¹(102-digit number)

13168387817632291564…15866352688574402561

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

2.633 × 10¹⁰¹(102-digit number)

26336775635264583129…31732705377148805119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.633 × 10¹⁰¹(102-digit number)

26336775635264583129…31732705377148805121

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

5.267 × 10¹⁰¹(102-digit number)

52673551270529166259…63465410754297610239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.267 × 10¹⁰¹(102-digit number)

52673551270529166259…63465410754297610241

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