Block #418,770

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 3:36:54 AM · Difficulty 10.3838 · 6,377,374 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1612d3c881d0866e31c103e79fdc26d92709e8b21161cbf0a4876a672c74685f

View on Chainz ↗

Height

#418,770

Difficulty

10.383774

Transactions

Size

1.09 KB

Version

Bits

0a623f0b

Nonce

43,423,037

Timestamp

2/25/2014, 3:36:54 AM

Confirmations

6,377,374

Mined by

⛏️ P2SHAd8du5pJSgesvhgzDeBAjBuFiD4XiauooU

Merkle Root

030c3cae5aecf481d19045fb9969082f8a477d881689b29a3e66a10f832b1769

Transactions (2)

Coinbase451fbd2eb5c4f0…300b582dd497ac

1 in → 1 out9.2700 XPM110 B

Ad8du5pJ…4XiauooU

41bd00fcbff048…1ae57f5df09476

5 in → 7 out19.3809 XPM919 B

ASY8qdEN…UpVsn1mm AeKNrjNj…1NEq95Ta AMmkoL9c…RfSSCaRk ARfLPGkP…TLd7khVD AMurAYrb…3iomaSF2

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.

4.248 × 10⁹⁸(99-digit number)

42482563385871303180…29665999048304230399

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

4.248 × 10⁹⁸(99-digit number)

42482563385871303180…29665999048304230399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.248 × 10⁹⁸(99-digit number)

42482563385871303180…29665999048304230401

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

8.496 × 10⁹⁸(99-digit number)

84965126771742606360…59331998096608460799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.496 × 10⁹⁸(99-digit number)

84965126771742606360…59331998096608460801

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

1.699 × 10⁹⁹(100-digit number)

16993025354348521272…18663996193216921599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.699 × 10⁹⁹(100-digit number)

16993025354348521272…18663996193216921601

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

3.398 × 10⁹⁹(100-digit number)

33986050708697042544…37327992386433843199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.398 × 10⁹⁹(100-digit number)

33986050708697042544…37327992386433843201

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

6.797 × 10⁹⁹(100-digit number)

67972101417394085088…74655984772867686399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.797 × 10⁹⁹(100-digit number)

67972101417394085088…74655984772867686401

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