Block #1,595,097

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/22/2016, 8:03:58 AM · Difficulty 10.6242 · 5,220,725 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

940a6f1d0a360f1a566d4a7ac07551114aaf2829e80f4723d8bad9d76fd72c10

View on Chainz ↗

Height

#1,595,097

Difficulty

10.624191

Transactions

Size

971 B

Version

Bits

0a9fcafc

Nonce

260,234,775

Timestamp

5/22/2016, 8:03:58 AM

Confirmations

5,220,725

Mined by

⛏️ P2SHAWyW4VgbJYzYyc5TK8gAKQh9Y9DUWv5NYU

Merkle Root

a7ad2bbb882b31dd43041afaacef6b65f30bb307fd490ed9b1ec951c056e189c

Transactions (2)

Coinbase9e5564fbee06cd…f48f5018331b2f

1 in → 1 out8.8600 XPM109 B

AWyW4Vgb…DUWv5NYU

73c73987b9db64…87a3915449d190

1 in → 18 out59.5745 XPM771 B

AYn1BPVv…yk4QpbYs AHEKpgj1…fUbeXF2i AMLbGJkL…gz2yUcR8 AMuEYzSo…Gmd5PTKP AMJsR7Zo…MJV42TZM

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.

2.692 × 10⁹⁷(98-digit number)

26923093336973026377…97248412294706626559

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

2.692 × 10⁹⁷(98-digit number)

26923093336973026377…97248412294706626559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.692 × 10⁹⁷(98-digit number)

26923093336973026377…97248412294706626561

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

5.384 × 10⁹⁷(98-digit number)

53846186673946052755…94496824589413253119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.384 × 10⁹⁷(98-digit number)

53846186673946052755…94496824589413253121

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

1.076 × 10⁹⁸(99-digit number)

10769237334789210551…88993649178826506239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.076 × 10⁹⁸(99-digit number)

10769237334789210551…88993649178826506241

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

2.153 × 10⁹⁸(99-digit number)

21538474669578421102…77987298357653012479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.153 × 10⁹⁸(99-digit number)

21538474669578421102…77987298357653012481

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

4.307 × 10⁹⁸(99-digit number)

43076949339156842204…55974596715306024959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.307 × 10⁹⁸(99-digit number)

43076949339156842204…55974596715306024961

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 #1,595,097

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