Block #1,085,809

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/1/2015, 6:44:37 PM · Difficulty 10.7558 · 5,719,391 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f2b21ac25694917a292ecef8157ebf91fb2a3432aa35105095a9acc50de87111

View on Chainz ↗

Height

#1,085,809

Difficulty

10.755752

Transactions

Size

945 B

Version

Bits

0ac178f5

Nonce

971,536,075

Timestamp

6/1/2015, 6:44:37 PM

Confirmations

5,719,391

Mined by

⛏️ P2SHAHUms6TjFmBozQKJcQmjDWUZ7nEG1HszhZ

Merkle Root

66c5548abf702eedd9b13bf8ae2ab3abeef3024fa593d227614c6573e2b826b3

Transactions (3)

Coinbasec39d6926c070c2…1c9c3ff28752e2

1 in → 1 out8.6500 XPM109 B

AHUms6Tj…EG1HszhZ

a7bb35f85cdcbb…2199dc8ffab4fc

3 in → 2 out50.0100 XPM520 B

ARmsZ5b1…ADJ2hHPd AammczUF…DSFMcBo7

a50e791d7622fb…2c2e14332b28c0

1 in → 2 out8.6000 XPM226 B

AHmcchxr…vBbydp5n AVugURve…k3humkZX

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.

4.522 × 10⁹⁵(96-digit number)

45226649499189719575…35566693879859775999

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

4.522 × 10⁹⁵(96-digit number)

45226649499189719575…35566693879859775999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.522 × 10⁹⁵(96-digit number)

45226649499189719575…35566693879859776001

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

9.045 × 10⁹⁵(96-digit number)

90453298998379439151…71133387759719551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.045 × 10⁹⁵(96-digit number)

90453298998379439151…71133387759719552001

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

1.809 × 10⁹⁶(97-digit number)

18090659799675887830…42266775519439103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.809 × 10⁹⁶(97-digit number)

18090659799675887830…42266775519439104001

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

3.618 × 10⁹⁶(97-digit number)

36181319599351775660…84533551038878207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.618 × 10⁹⁶(97-digit number)

36181319599351775660…84533551038878208001

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

7.236 × 10⁹⁶(97-digit number)

72362639198703551321…69067102077756415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.236 × 10⁹⁶(97-digit number)

72362639198703551321…69067102077756416001

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