Block #421,731

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2014, 6:28:46 AM · Difficulty 10.3741 · 6,383,629 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

25942803365c5948390128525e7bb3ae902b84b65769eeb86238406752ed73d4

View on Chainz ↗

Height

#421,731

Difficulty

10.374055

Transactions

Size

881 B

Version

Bits

0a5fc20a

Nonce

200,148

Timestamp

2/27/2014, 6:28:46 AM

Confirmations

6,383,629

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4d2c4794f692d12316ddea4b15ac303c3f77e5c39cff6d8aef78401fe77a334d

Transactions (4)

Coinbasee6192e27b1d170…870479493e660e

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

a0119467a60df9…a1f961bddbe9a7

1 in → 2 out9.1900 XPM226 B

AGdVDGjk…Xf5GHjQ2 AXZ78owx…Uxt7V5XX

c93e2a6a890a77…d7bb773057ccd4

1 in → 2 out9.1900 XPM225 B

AQHAqvD2…SyJfBr2H AUq6f9hu…XXF5HtBq

8d60de74ac7c48…6f824e7df58f2e

1 in → 2 out9.1900 XPM227 B

APdGMwfe…THN8fpwr ARZ9w5Nr…c8A4keKY

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.

3.009 × 10¹⁰¹(102-digit number)

30097926595416771029…40123848176171548799

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

3.009 × 10¹⁰¹(102-digit number)

30097926595416771029…40123848176171548799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.009 × 10¹⁰¹(102-digit number)

30097926595416771029…40123848176171548801

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

6.019 × 10¹⁰¹(102-digit number)

60195853190833542058…80247696352343097599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.019 × 10¹⁰¹(102-digit number)

60195853190833542058…80247696352343097601

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

1.203 × 10¹⁰²(103-digit number)

12039170638166708411…60495392704686195199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.203 × 10¹⁰²(103-digit number)

12039170638166708411…60495392704686195201

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

2.407 × 10¹⁰²(103-digit number)

24078341276333416823…20990785409372390399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.407 × 10¹⁰²(103-digit number)

24078341276333416823…20990785409372390401

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

4.815 × 10¹⁰²(103-digit number)

48156682552666833646…41981570818744780799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.815 × 10¹⁰²(103-digit number)

48156682552666833646…41981570818744780801

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