Block #431,893

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 12:37:07 PM · Difficulty 10.3427 · 6,364,553 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

263d89927bb3e37f51d015596741c82a11c110a1fe9c39d50d2a78a871441ca0

View on Chainz ↗

Height

#431,893

Difficulty

10.342736

Transactions

Size

911 B

Version

Bits

0a57bd8f

Nonce

398,150

Timestamp

3/6/2014, 12:37:07 PM

Confirmations

6,364,553

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7af594fc674d5d0f7b3d55e00ce8ecaa08abfdc4564389c412400905d3bd12ab

Transactions (3)

Coinbasecf9ceb56dbfd02…71bfcd8ba980b1

1 in → 1 out9.3500 XPM116 B

AbwWkWZt…kawDhufa

a28d666e8953f3…2f1e22199caa03

2 in → 7 out18.6700 XPM477 B

Aaw3phCR…9mHC1CxX AJ2a8S3W…tqXNT8d1 AMw6Dcr2…pMu8K6Zs Ad7xsVzr…4sfLgXsD AbABGh95…BpJH6dHp

2be2a5c0c21fab…a737acdf36d01f

1 in → 2 out83.4034 XPM225 B

AFvJqUdQ…ZKwWQdad AGVLqZBp…4EAru9ja

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.

4.538 × 10¹⁰²(103-digit number)

45382901040445740460…43900511675502514819

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

4.538 × 10¹⁰²(103-digit number)

45382901040445740460…43900511675502514819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.538 × 10¹⁰²(103-digit number)

45382901040445740460…43900511675502514821

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

9.076 × 10¹⁰²(103-digit number)

90765802080891480921…87801023351005029639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.076 × 10¹⁰²(103-digit number)

90765802080891480921…87801023351005029641

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

1.815 × 10¹⁰³(104-digit number)

18153160416178296184…75602046702010059279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.815 × 10¹⁰³(104-digit number)

18153160416178296184…75602046702010059281

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

3.630 × 10¹⁰³(104-digit number)

36306320832356592368…51204093404020118559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.630 × 10¹⁰³(104-digit number)

36306320832356592368…51204093404020118561

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

7.261 × 10¹⁰³(104-digit number)

72612641664713184737…02408186808040237119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.261 × 10¹⁰³(104-digit number)

72612641664713184737…02408186808040237121

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