Block #2,098,226

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2017, 9:42:58 AM · Difficulty 10.8663 · 4,745,031 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62804d63c66242a5931eb28fdaf89b498decbb2a67480ceefe35af2b4591398a

View on Chainz ↗

Height

#2,098,226

Difficulty

10.866294

Transactions

Size

963 B

Version

Bits

0addc572

Nonce

1,049,217,189

Timestamp

5/3/2017, 9:42:58 AM

Confirmations

4,745,031

Mined by

⛏️ P2SHAST2bczjj8nLhByCWZnAEyugWJUwAQ7LYk

Merkle Root

8b6ae986ebeff3003c161793219ed14000e9f34be05dbfe79cd0d8cb3c4a06dc

Transactions (2)

Coinbased2e99693335d21…c9fcfee60fd40d

1 in → 1 out8.4700 XPM109 B

AST2bczj…UwAQ7LYk

b39bc347499c26…615cc24c8ca81f

6 in → 2 out50.8000 XPM763 B

AG3yMnVp…7zjjypic AcnBQbfU…ucZMpseM

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.

2.370 × 10⁹⁶(97-digit number)

23706005308167968014…23906214507769036799

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

2.370 × 10⁹⁶(97-digit number)

23706005308167968014…23906214507769036799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.370 × 10⁹⁶(97-digit number)

23706005308167968014…23906214507769036801

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

4.741 × 10⁹⁶(97-digit number)

47412010616335936028…47812429015538073599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.741 × 10⁹⁶(97-digit number)

47412010616335936028…47812429015538073601

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

9.482 × 10⁹⁶(97-digit number)

94824021232671872057…95624858031076147199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.482 × 10⁹⁶(97-digit number)

94824021232671872057…95624858031076147201

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

1.896 × 10⁹⁷(98-digit number)

18964804246534374411…91249716062152294399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.896 × 10⁹⁷(98-digit number)

18964804246534374411…91249716062152294401

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

3.792 × 10⁹⁷(98-digit number)

37929608493068748822…82499432124304588799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.792 × 10⁹⁷(98-digit number)

37929608493068748822…82499432124304588801

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 #2,098,226

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