Block #1,593,966

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/21/2016, 12:09:48 PM · Difficulty 10.6288 · 5,232,995 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09e5cc5240f8a6ed65d0c545d9f96aefa26ce16495933dca50aea32fa51e1dd5

View on Chainz ↗

Height

#1,593,966

Difficulty

10.628849

Transactions

Size

1.08 KB

Version

Bits

0aa0fc43

Nonce

669,123,716

Timestamp

5/21/2016, 12:09:48 PM

Confirmations

5,232,995

Mined by

⛏️ P2SHAXFXCfj2JoyPfMrtqSh3C9mLrdtKyePFNK

Merkle Root

bf3a37eea9346776a2c1f671d3b2b71fc5ee5456ea76f32d63113507860413c7

Transactions (2)

Coinbaseca169c3ef7dd11…cfb2a44481d89f

1 in → 1 out8.8500 XPM109 B

AXFXCfj2…tKyePFNK

7b2def3fcb32c4…9a370d143671d5

1 in → 22 out78.8501 XPM907 B

AUJFJ1f1…WanXjapy ANzvisbf…aWVodmgs ARM6k7wL…sZ48m8mA Ac9HqP8y…nj4GmPmr ASCduurY…jm3YuXrf

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.

3.326 × 10⁹⁷(98-digit number)

33264504299466998506…80381178175481446399

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

3.326 × 10⁹⁷(98-digit number)

33264504299466998506…80381178175481446399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.326 × 10⁹⁷(98-digit number)

33264504299466998506…80381178175481446401

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

6.652 × 10⁹⁷(98-digit number)

66529008598933997013…60762356350962892799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.652 × 10⁹⁷(98-digit number)

66529008598933997013…60762356350962892801

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

1.330 × 10⁹⁸(99-digit number)

13305801719786799402…21524712701925785599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.330 × 10⁹⁸(99-digit number)

13305801719786799402…21524712701925785601

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

2.661 × 10⁹⁸(99-digit number)

26611603439573598805…43049425403851571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.661 × 10⁹⁸(99-digit number)

26611603439573598805…43049425403851571201

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

5.322 × 10⁹⁸(99-digit number)

53223206879147197611…86098850807703142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.322 × 10⁹⁸(99-digit number)

53223206879147197611…86098850807703142401

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 #1,593,966

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