Block #437,920

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 3:19:50 PM · Difficulty 10.3597 · 6,370,079 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8bbc16a82a94afc582ddcab77c8b7a5df3dff2b2b72d835f0998408ef36ad51

View on Chainz ↗

Height

#437,920

Difficulty

10.359669

Transactions

Size

395 B

Version

Bits

0a5c1342

Nonce

17,482

Timestamp

3/10/2014, 3:19:50 PM

Confirmations

6,370,079

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

3bd7a8f87925095f7bb61bb53ee637bbda26f055eb743c862f2dc679ec080756

Transactions (2)

Coinbase5678763925ecc6…b36952243d9b17

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

317ec0164fff57…b578e8175b535c

1 in → 1 out4.9937 XPM192 B

AepBuXhC…nuU7jDvn

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.

8.069 × 10¹⁰²(103-digit number)

80690767158156792530…39378989900082297439

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

8.069 × 10¹⁰²(103-digit number)

80690767158156792530…39378989900082297439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.069 × 10¹⁰²(103-digit number)

80690767158156792530…39378989900082297441

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

1.613 × 10¹⁰³(104-digit number)

16138153431631358506…78757979800164594879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.613 × 10¹⁰³(104-digit number)

16138153431631358506…78757979800164594881

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

3.227 × 10¹⁰³(104-digit number)

32276306863262717012…57515959600329189759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.227 × 10¹⁰³(104-digit number)

32276306863262717012…57515959600329189761

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

6.455 × 10¹⁰³(104-digit number)

64552613726525434024…15031919200658379519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.455 × 10¹⁰³(104-digit number)

64552613726525434024…15031919200658379521

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

1.291 × 10¹⁰⁴(105-digit number)

12910522745305086804…30063838401316759039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.291 × 10¹⁰⁴(105-digit number)

12910522745305086804…30063838401316759041

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 #437,920

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