Block #185,110

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 2:03:49 AM · Difficulty 9.8622 · 6,609,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f95445415e5294fbc848a36ae0f0ead034142a892bc341d510be4e28d48d89c

View on Chainz ↗

Height

#185,110

Difficulty

9.862193

Transactions

Size

615 B

Version

Bits

09dcb8b3

Nonce

21,538

Timestamp

9/29/2013, 2:03:49 AM

Confirmations

6,609,511

Mined by

⛏️ P2SHAJQc8VozgN2SnbZdZgMjNzShT96N7hBoJq

Merkle Root

e304895735d931a8ebf0b4e67289554342b67f88c4249971ffddc72c1d1d7bf4

Transactions (3)

Coinbase46e71ec5881072…d308cdfa8e4068

1 in → 1 out10.2900 XPM109 B

AJQc8Voz…6N7hBoJq

2a6c9fe81f823d…9c35ba8ffee59b

1 in → 1 out3.0534 XPM191 B

Abwo4U7S…WXQvKS2P

ca6a43b429111f…f6ef627866fc69

1 in → 2 out2.0712 XPM225 B

AV92kqEm…P3wLDQbm AMmGeXac…8N1iWEtv

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.

5.279 × 10⁹⁵(96-digit number)

52790615650473314356…29431069797824448079

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

5.279 × 10⁹⁵(96-digit number)

52790615650473314356…29431069797824448079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.279 × 10⁹⁵(96-digit number)

52790615650473314356…29431069797824448081

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

1.055 × 10⁹⁶(97-digit number)

10558123130094662871…58862139595648896159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.055 × 10⁹⁶(97-digit number)

10558123130094662871…58862139595648896161

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

2.111 × 10⁹⁶(97-digit number)

21116246260189325742…17724279191297792319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.111 × 10⁹⁶(97-digit number)

21116246260189325742…17724279191297792321

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

4.223 × 10⁹⁶(97-digit number)

42232492520378651485…35448558382595584639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.223 × 10⁹⁶(97-digit number)

42232492520378651485…35448558382595584641

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

8.446 × 10⁹⁶(97-digit number)

84464985040757302970…70897116765191169279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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