Block #1,195,886

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/16/2015, 12:41:40 AM · Difficulty 10.8333 · 5,616,557 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5962f1ab358179e50683fd58e85ff7229691e44fc9bce91f0da33a68d61b3ae

View on Chainz ↗

Height

#1,195,886

Difficulty

10.833284

Transactions

Size

3.97 KB

Version

Bits

0ad5521d

Nonce

1,689,421,121

Timestamp

8/16/2015, 12:41:40 AM

Confirmations

5,616,557

Mined by

⛏️ P2SHAPXj7LFeXwk5dqB2kP7n9dF2DojAY4zKe2

Merkle Root

05893d381eb7c257795cc8e980e1772fe8b89f7caa0142ad4a6adecf6d6ddd65

Transactions (5)

Coinbase7905a38386d820…408158f9e9defc

1 in → 1 out8.5900 XPM110 B

APXj7LFe…jAY4zKe2

d97977b0ab64e4…b2dc78c96fd55d

1 in → 2 out8.4000 XPM227 B

AXrTw46X…e1dGvSFf AGfNBEyV…eA6aSjVY

480b359b179ae0…8a6453c36bf533

2 in → 2 out16.9000 XPM376 B

AY8iGrh6…oUDeSVqa ALkQAjXt…bRhHvroX

6fa4666ffe7cc9…6e9831beb07240

6 in → 2 out10.0724 XPM963 B

AQRAerBs…hpxYWDNz AKTd6ocn…Ewwo3nj2

27296741c613f4…f698ccf5b88c46

15 in → 2 out154.6344 XPM2.24 KB

AJVeRHXf…C2yREH1f ANiLyPku…SraNHGg2

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.

1.677 × 10⁹⁶(97-digit number)

16777582019510574115…42901738571351166719

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

1.677 × 10⁹⁶(97-digit number)

16777582019510574115…42901738571351166719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.677 × 10⁹⁶(97-digit number)

16777582019510574115…42901738571351166721

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

3.355 × 10⁹⁶(97-digit number)

33555164039021148230…85803477142702333439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.355 × 10⁹⁶(97-digit number)

33555164039021148230…85803477142702333441

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

6.711 × 10⁹⁶(97-digit number)

67110328078042296460…71606954285404666879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.711 × 10⁹⁶(97-digit number)

67110328078042296460…71606954285404666881

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

1.342 × 10⁹⁷(98-digit number)

13422065615608459292…43213908570809333759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.342 × 10⁹⁷(98-digit number)

13422065615608459292…43213908570809333761

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

2.684 × 10⁹⁷(98-digit number)

26844131231216918584…86427817141618667519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.684 × 10⁹⁷(98-digit number)

26844131231216918584…86427817141618667521

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 #1,195,886

Cookie Preferences