Block #437,309

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 5:17:37 AM · Difficulty 10.3581 · 6,389,400 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e56bc6267fc054bdb0bd318ff4484c43a08e0b1a919b6692517e08e070fa16db

View on Chainz ↗

Height

#437,309

Difficulty

10.358060

Transactions

Size

3.89 KB

Version

Bits

0a5ba9d3

Nonce

195,594

Timestamp

3/10/2014, 5:17:37 AM

Confirmations

6,389,400

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

904931f85f5c061390447c982bbe6564effdbd5456bfd64d1f908351db6dea55

Transactions (2)

Coinbase60a26f2f22a4ee…e7bc9c2279ca79

1 in → 1 out9.3500 XPM116 B

AbwWkWZt…kawDhufa

824d8fb40af5b9…11683991d2dfab

25 in → 2 out8.0971 XPM3.69 KB

AXvfTQnC…2EY9iDjK AX32q3uJ…ZpKTUZ4U

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.

4.462 × 10⁹⁹(100-digit number)

44622564017137559101…17648569964078074879

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

4.462 × 10⁹⁹(100-digit number)

44622564017137559101…17648569964078074879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.462 × 10⁹⁹(100-digit number)

44622564017137559101…17648569964078074881

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

8.924 × 10⁹⁹(100-digit number)

89245128034275118202…35297139928156149759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.924 × 10⁹⁹(100-digit number)

89245128034275118202…35297139928156149761

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

1.784 × 10¹⁰⁰(101-digit number)

17849025606855023640…70594279856312299519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.784 × 10¹⁰⁰(101-digit number)

17849025606855023640…70594279856312299521

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

3.569 × 10¹⁰⁰(101-digit number)

35698051213710047280…41188559712624599039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.569 × 10¹⁰⁰(101-digit number)

35698051213710047280…41188559712624599041

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

7.139 × 10¹⁰⁰(101-digit number)

71396102427420094561…82377119425249198079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.139 × 10¹⁰⁰(101-digit number)

71396102427420094561…82377119425249198081

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 #437,309

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