Block #428,521

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 3:48:32 AM · Difficulty 10.3454 · 6,367,021 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3f47a5b0a60c4334f248d51e65dcdd6478a14b35f1657edd6b4daba82b7b746

View on Chainz ↗

Height

#428,521

Difficulty

10.345415

Transactions

Size

1.44 KB

Version

Bits

0a586d1d

Nonce

290,621

Timestamp

3/4/2014, 3:48:32 AM

Confirmations

6,367,021

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

b0e1dcabd71ef5cd32a2e56137133a86bd15a4182106033fd86b3f65b35991fc

Transactions (2)

Coinbase6ca11145596d4a…31d0825b3c3f3d

1 in → 1 out9.3500 XPM110 B

AeKNrjNj…1NEq95Ta

c8233c6bae8b2a…37807e062e9451

6 in → 16 out46.9463 XPM1.24 KB

AHhc5Xug…zUHKfPCk AZR87GPa…sk2Dbvx4 AFw4uFDH…ykrLVsJg AW7d3yxi…SwRe461r ARobqFaw…sqUDMdNr

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.

1.919 × 10⁹⁵(96-digit number)

19194568774070234779…34766256672245791599

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

1.919 × 10⁹⁵(96-digit number)

19194568774070234779…34766256672245791599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.919 × 10⁹⁵(96-digit number)

19194568774070234779…34766256672245791601

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

3.838 × 10⁹⁵(96-digit number)

38389137548140469558…69532513344491583199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.838 × 10⁹⁵(96-digit number)

38389137548140469558…69532513344491583201

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

7.677 × 10⁹⁵(96-digit number)

76778275096280939117…39065026688983166399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.677 × 10⁹⁵(96-digit number)

76778275096280939117…39065026688983166401

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

1.535 × 10⁹⁶(97-digit number)

15355655019256187823…78130053377966332799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.535 × 10⁹⁶(97-digit number)

15355655019256187823…78130053377966332801

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

3.071 × 10⁹⁶(97-digit number)

30711310038512375647…56260106755932665599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.071 × 10⁹⁶(97-digit number)

30711310038512375647…56260106755932665601

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