Block #2,159,789

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/14/2017, 2:37:14 AM · Difficulty 10.9027 · 4,671,450 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6d93ec341ab2a05ac6086e59d95b405fa6f5de5bc485f42502d75aff2c882fa7

View on Chainz ↗

Height

#2,159,789

Difficulty

10.902707

Transactions

Size

1.57 KB

Version

Bits

0ae717d0

Nonce

1,519,704,516

Timestamp

6/14/2017, 2:37:14 AM

Confirmations

4,671,450

Mined by

⛏️ P2SHAMeYiE5GN8KUyCZb3gwSVFropAyrCujUVJ

Merkle Root

c3628a6ec20c59bafb8a8ea44f4ccddecb2014ce3cf2b6a2690cfa921a67ff98

Transactions (2)

Coinbase618bfe6b8be8c5…8bf7f837356e11

1 in → 1 out8.4200 XPM109 B

AMeYiE5G…yrCujUVJ

9b1e103902f9ec…056ceceac29cc6

9 in → 2 out2629.3534 XPM1.38 KB

APsQSb88…wuccNFXN AN9uTUbg…2PCYBhoq

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.

5.190 × 10⁹⁵(96-digit number)

51902076512780433587…25374323790723596799

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

5.190 × 10⁹⁵(96-digit number)

51902076512780433587…25374323790723596799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.190 × 10⁹⁵(96-digit number)

51902076512780433587…25374323790723596801

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

1.038 × 10⁹⁶(97-digit number)

10380415302556086717…50748647581447193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.038 × 10⁹⁶(97-digit number)

10380415302556086717…50748647581447193601

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

2.076 × 10⁹⁶(97-digit number)

20760830605112173435…01497295162894387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.076 × 10⁹⁶(97-digit number)

20760830605112173435…01497295162894387201

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

4.152 × 10⁹⁶(97-digit number)

41521661210224346870…02994590325788774399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.152 × 10⁹⁶(97-digit number)

41521661210224346870…02994590325788774401

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

8.304 × 10⁹⁶(97-digit number)

83043322420448693740…05989180651577548799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.304 × 10⁹⁶(97-digit number)

83043322420448693740…05989180651577548801

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 #2,159,789

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