Block #1,270,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/7/2015, 7:05:28 AM · Difficulty 10.8160 · 5,556,409 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

430bd8262fd58bbdb05c1cb285ec14fa8eb5ad541f79ddb5b65a3f22cb462055

View on Chainz ↗

Height

#1,270,595

Difficulty

10.816023

Transactions

Size

900 B

Version

Bits

0ad0e6df

Nonce

125,467,288

Timestamp

10/7/2015, 7:05:28 AM

Confirmations

5,556,409

Mined by

⛏️ P2SHAJVmbiyMUc2sNcBqw5hu8avTBPMvC2eyfJ

Merkle Root

2682bd9998fecbea6b8434893b05ecfc28aecb38990d83ddafc2163779ecfbff

Transactions (2)

Coinbasebc00e4859718a2…5c97da6676e066

1 in → 1 out8.5400 XPM110 B

AJVmbiyM…MvC2eyfJ

746defac91cde0…6d80b34d3b7146

1 in → 16 out45.5324 XPM701 B

AahNe9Eb…j7WvUkU7 AXCVMrY2…W1HDjsk4 AdXaUrde…ZoizVcpy AYWX1XvG…vZ4aaLio ASv8QCCi…HPGBuiyg

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.

2.540 × 10⁹³(94-digit number)

25407718594345755887…46650504483317311439

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

2.540 × 10⁹³(94-digit number)

25407718594345755887…46650504483317311439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.540 × 10⁹³(94-digit number)

25407718594345755887…46650504483317311441

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

5.081 × 10⁹³(94-digit number)

50815437188691511775…93301008966634622879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.081 × 10⁹³(94-digit number)

50815437188691511775…93301008966634622881

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

1.016 × 10⁹⁴(95-digit number)

10163087437738302355…86602017933269245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.016 × 10⁹⁴(95-digit number)

10163087437738302355…86602017933269245761

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

2.032 × 10⁹⁴(95-digit number)

20326174875476604710…73204035866538491519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.032 × 10⁹⁴(95-digit number)

20326174875476604710…73204035866538491521

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

4.065 × 10⁹⁴(95-digit number)

40652349750953209420…46408071733076983039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.065 × 10⁹⁴(95-digit number)

40652349750953209420…46408071733076983041

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 #1,270,595

Cookie Preferences