Block #443,402

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 1:03:16 PM · Difficulty 10.3447 · 6,359,100 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81514e7cc2b39213677872821d0493635ab97db403c56e7a657c7ebc095ff196

View on Chainz ↗

Height

#443,402

Difficulty

10.344719

Transactions

Size

31.85 KB

Version

Bits

0a583f7c

Nonce

182,393

Timestamp

3/14/2014, 1:03:16 PM

Confirmations

6,359,100

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

b8e81b5a97c33d6b6bf8c37e090dec88fcfc55fc0e0e711273c155b9967bf6e7

Transactions (5)

Coinbasedbefd11ecea764…117dbacc47a1f9

1 in → 1 out9.6700 XPM110 B

AeKNrjNj…1NEq95Ta

092af821e769ce…be06b6eb56002d

5 in → 1 out1865.4520 XPM786 B

AKhUoqKQ…6QS8kzdx

8b3d1527124b83…249d639094c740

11 in → 2 out33.0555 XPM1.67 KB

AWYuJMwV…aht6Ktx3 ALy7eC9P…Ku5XZv3s

b224367108552e…b36e05ee445a01

200 in → 2 out66.0102 XPM28.99 KB

AaMB4DVX…HKboTGBY AGwg6tEm…Fsz3FW5B

f140cb1514ad22…15eb6c9b1ac45b

1 in → 2 out4.1769 XPM227 B

AdS5dDv6…Tf5QZx3Q AQXbnpiH…icP9VFRm

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.

1.332 × 10⁹⁸(99-digit number)

13323733938161957897…31670759828338943999

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

1.332 × 10⁹⁸(99-digit number)

13323733938161957897…31670759828338943999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.332 × 10⁹⁸(99-digit number)

13323733938161957897…31670759828338944001

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

2.664 × 10⁹⁸(99-digit number)

26647467876323915795…63341519656677887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.664 × 10⁹⁸(99-digit number)

26647467876323915795…63341519656677888001

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

5.329 × 10⁹⁸(99-digit number)

53294935752647831590…26683039313355775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.329 × 10⁹⁸(99-digit number)

53294935752647831590…26683039313355776001

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

1.065 × 10⁹⁹(100-digit number)

10658987150529566318…53366078626711551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.065 × 10⁹⁹(100-digit number)

10658987150529566318…53366078626711552001

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

2.131 × 10⁹⁹(100-digit number)

21317974301059132636…06732157253423103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.131 × 10⁹⁹(100-digit number)

21317974301059132636…06732157253423104001

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