Block #1,667,640

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/10/2016, 11:32:25 PM · Difficulty 10.6979 · 5,175,389 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bbda1326ee134445bcedf5a930d0efcfb1770fdc367badd89e65224d82285ddd

View on Chainz ↗

Height

#1,667,640

Difficulty

10.697948

Transactions

Size

9.17 KB

Version

Bits

0ab2acbe

Nonce

1,143,911,116

Timestamp

7/10/2016, 11:32:25 PM

Confirmations

5,175,389

Mined by

⛏️ P2SHAZHzfQWURC7tf738mavqdJfnmrwfANDJky

Merkle Root

b78290bb8552fcb49a40de44b951410cdcae16d44e0facda7a56cb61c98d7808

Transactions (2)

Coinbase667c4cb3d8e85a…d854d33978a68d

1 in → 1 out8.8200 XPM110 B

AZHzfQWU…wfANDJky

11ae9a6cf5b396…75cddc920e559e

79 in → 2 out661.0205 XPM8.97 KB

AVAvXJDG…boW6hx49 AV5QB4JM…SDyBHapL

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.

2.569 × 10⁹⁵(96-digit number)

25691653123995663755…92353585903979349759

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

2.569 × 10⁹⁵(96-digit number)

25691653123995663755…92353585903979349759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.569 × 10⁹⁵(96-digit number)

25691653123995663755…92353585903979349761

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

5.138 × 10⁹⁵(96-digit number)

51383306247991327510…84707171807958699519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.138 × 10⁹⁵(96-digit number)

51383306247991327510…84707171807958699521

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

1.027 × 10⁹⁶(97-digit number)

10276661249598265502…69414343615917399039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.027 × 10⁹⁶(97-digit number)

10276661249598265502…69414343615917399041

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

2.055 × 10⁹⁶(97-digit number)

20553322499196531004…38828687231834798079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.055 × 10⁹⁶(97-digit number)

20553322499196531004…38828687231834798081

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

4.110 × 10⁹⁶(97-digit number)

41106644998393062008…77657374463669596159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.110 × 10⁹⁶(97-digit number)

41106644998393062008…77657374463669596161

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

Block #1,667,640

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