Block #2,128,710

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2017, 2:15:20 AM · Difficulty 10.9132 · 4,703,645 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

250cffa65612f8f0042651c90827364a3aab97d02da09a5887a3287a18f03f34

View on Chainz ↗

Height

#2,128,710

Difficulty

10.913195

Transactions

Size

597 B

Version

Bits

0ae9c71e

Nonce

1,834,338,583

Timestamp

5/23/2017, 2:15:20 AM

Confirmations

4,703,645

Mined by

⛏️ P2SHAWQ5SLUMHNsYw3FvqR7XjdQAf7joDFudJv

Merkle Root

d674dc61fecac01024ee97d3a1508e9ffd865e2792b2c8ecaf9d1e92b026d3c0

Transactions (2)

Coinbase357c3c0f4bd166…d143130e9540f1

1 in → 1 out8.3900 XPM110 B

AWQ5SLUM…joDFudJv

226718895e8178…d439c35b574796

1 in → 7 out0.6386 XPM397 B

AK9xqso1…GdGESuXs AakWoM5K…tba37cYB AL8hLFRk…5p2eV5gV APKKh5H7…ZFRuwXrr ATtEPvyb…QAmLTma4

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.

1.319 × 10⁹⁵(96-digit number)

13191376927544756805…74505964144218931199

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

1.319 × 10⁹⁵(96-digit number)

13191376927544756805…74505964144218931199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.319 × 10⁹⁵(96-digit number)

13191376927544756805…74505964144218931201

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

2.638 × 10⁹⁵(96-digit number)

26382753855089513610…49011928288437862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.638 × 10⁹⁵(96-digit number)

26382753855089513610…49011928288437862401

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

5.276 × 10⁹⁵(96-digit number)

52765507710179027221…98023856576875724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.276 × 10⁹⁵(96-digit number)

52765507710179027221…98023856576875724801

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

1.055 × 10⁹⁶(97-digit number)

10553101542035805444…96047713153751449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.055 × 10⁹⁶(97-digit number)

10553101542035805444…96047713153751449601

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

2.110 × 10⁹⁶(97-digit number)

21106203084071610888…92095426307502899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.110 × 10⁹⁶(97-digit number)

21106203084071610888…92095426307502899201

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 #2,128,710

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