Block #452,552

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 4:05:40 PM · Difficulty 10.3906 · 6,346,472 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

143ec767d82940d303b87ecc70517b86639b8c2921965e1865baa61361ee6439

View on Chainz ↗

Height

#452,552

Difficulty

10.390581

Transactions

Size

968 B

Version

Bits

0a63fd21

Nonce

95,401

Timestamp

3/20/2014, 4:05:40 PM

Confirmations

6,346,472

Mined by

⛏️ aS+\AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9ffe50faa27d332499f4c9ee72be38027818a220eeb5bb19020f26618da64b1a

Transactions (1)

Coinbase9ffe50faa27d33…0f26618da64b1a

1 in → 24 out9.2500 XPM879 B

AQvZBsUo…hppgRZTJ AScAzqGc…BZ6tV1vJ ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq AMm3qeod…8PBiCMXU

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.

3.110 × 10⁹³(94-digit number)

31105995311762143095…96965806883692109699

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

3.110 × 10⁹³(94-digit number)

31105995311762143095…96965806883692109699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.110 × 10⁹³(94-digit number)

31105995311762143095…96965806883692109701

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

6.221 × 10⁹³(94-digit number)

62211990623524286191…93931613767384219399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.221 × 10⁹³(94-digit number)

62211990623524286191…93931613767384219401

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

1.244 × 10⁹⁴(95-digit number)

12442398124704857238…87863227534768438799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.244 × 10⁹⁴(95-digit number)

12442398124704857238…87863227534768438801

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

2.488 × 10⁹⁴(95-digit number)

24884796249409714476…75726455069536877599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.488 × 10⁹⁴(95-digit number)

24884796249409714476…75726455069536877601

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

4.976 × 10⁹⁴(95-digit number)

49769592498819428953…51452910139073755199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.976 × 10⁹⁴(95-digit number)

49769592498819428953…51452910139073755201

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