Block #1,595,404

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/22/2016, 2:08:34 PM · Difficulty 10.6201 · 5,229,185 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b4015179e1fd2ac7b68b433733d614802b422a8dc87b4453fc71c662b80fa71

View on Chainz ↗

Height

#1,595,404

Difficulty

10.620063

Transactions

Size

1.15 KB

Version

Bits

0a9ebc77

Nonce

505,239,373

Timestamp

5/22/2016, 2:08:34 PM

Confirmations

5,229,185

Mined by

⛏️ P2SHARrHaWzX8HxU9t6Z88tmCZw9ZV34E2sWD1

Merkle Root

7012f5e8e36c6438ffce5b307e91584f85983d7edd64071a390310921ffffa8f

Transactions (2)

Coinbase17d58d1e877baa…d70585c7dfb43d

1 in → 1 out8.8600 XPM110 B

ARrHaWzX…34E2sWD1

68f1cfadf6eb9c…b7220acc7a3e35

1 in → 24 out54.6619 XPM973 B

ARM6k7wL…sZ48m8mA AdMZman8…iRcw9p1T AeL98usR…DyTKf5wf AYVQ3hHz…Ce6whb4U AVbPDrE9…qY1ei75k

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.

4.791 × 10⁹⁷(98-digit number)

47919184333406068870…91739137512481535999

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

4.791 × 10⁹⁷(98-digit number)

47919184333406068870…91739137512481535999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.791 × 10⁹⁷(98-digit number)

47919184333406068870…91739137512481536001

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

9.583 × 10⁹⁷(98-digit number)

95838368666812137740…83478275024963071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.583 × 10⁹⁷(98-digit number)

95838368666812137740…83478275024963072001

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

1.916 × 10⁹⁸(99-digit number)

19167673733362427548…66956550049926143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.916 × 10⁹⁸(99-digit number)

19167673733362427548…66956550049926144001

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

3.833 × 10⁹⁸(99-digit number)

38335347466724855096…33913100099852287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.833 × 10⁹⁸(99-digit number)

38335347466724855096…33913100099852288001

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

7.667 × 10⁹⁸(99-digit number)

76670694933449710192…67826200199704575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.667 × 10⁹⁸(99-digit number)

76670694933449710192…67826200199704576001

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 #1,595,404

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