Block #451,196

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2014, 6:32:59 PM · Difficulty 10.3825 · 6,339,808 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

299b6815f995c67afa42c8c82f13aa72d2d2879500566a29d3ce30ccb85c0476

View on Chainz ↗

Height

#451,196

Difficulty

10.382537

Transactions

Size

652 B

Version

Bits

0a61edf3

Nonce

136,560

Timestamp

3/19/2014, 6:32:59 PM

Confirmations

6,339,808

Merkle Root

e5394b3503bfcd5e37f731c452e0d3081cbe56604599b48450467786365cdd00

Transactions (3)

Coinbasec387e9548319d3…dc3bcb5febff5c

1 in → 1 out9.2800 XPM110 B

AeKNrjNj…1NEq95Ta

909c99e6097d4a…57a69acdfcb930

1 in → 2 out6.2326 XPM225 B

Aec8Ncrw…6DdgG5z9 ALz3uSwR…DHKjj4EL

6ede8c9c15ac41…66ecda65629aab

1 in → 2 out1.6987 XPM226 B

ATEhhiKB…RxD17TvE AHbVCjv5…UKGNXKuQ

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.

5.652 × 10⁹⁷(98-digit number)

56526501645396274862…23318134451173697279

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

5.652 × 10⁹⁷(98-digit number)

56526501645396274862…23318134451173697279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.652 × 10⁹⁷(98-digit number)

56526501645396274862…23318134451173697281

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

1.130 × 10⁹⁸(99-digit number)

11305300329079254972…46636268902347394559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.130 × 10⁹⁸(99-digit number)

11305300329079254972…46636268902347394561

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

2.261 × 10⁹⁸(99-digit number)

22610600658158509945…93272537804694789119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.261 × 10⁹⁸(99-digit number)

22610600658158509945…93272537804694789121

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

4.522 × 10⁹⁸(99-digit number)

45221201316317019890…86545075609389578239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.522 × 10⁹⁸(99-digit number)

45221201316317019890…86545075609389578241

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

9.044 × 10⁹⁸(99-digit number)

90442402632634039780…73090151218779156479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.044 × 10⁹⁸(99-digit number)

90442402632634039780…73090151218779156481

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