Block #2,068,938

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2017, 6:45:49 AM · Difficulty 10.8568 · 4,771,192 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46d37f5be5180868b25fa13dc5ac743f745ced5be05ecc78de1dbde59ef0d826

View on Chainz ↗

Height

#2,068,938

Difficulty

10.856771

Transactions

Size

460 B

Version

Bits

0adb5560

Nonce

1,007,943,935

Timestamp

4/13/2017, 6:45:49 AM

Confirmations

4,771,192

Mined by

⛏️ P2SHAJhgmCFXepmiPJViPtbmCBD9MncxvR1cK8

Merkle Root

1e6b6dd8f8b9566af5caf6c21bee0e8bb375ebca1d904f26f3a1ab96f2a8c9cf

Transactions (2)

Coinbase642bfdf9d27fc5…307f6258348647

1 in → 1 out8.4800 XPM109 B

AJhgmCFX…cxvR1cK8

62ebd5c078ef9f…dd361c26539b7e

1 in → 3 out3.2398 XPM261 B

ARmvobPS…BpCMjd3J ANLSssep…jqjAdayc AJQLn2zM…pqLPEG4n

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.

1.903 × 10⁹⁵(96-digit number)

19036182058043227628…10122608111047147519

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

1.903 × 10⁹⁵(96-digit number)

19036182058043227628…10122608111047147519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.903 × 10⁹⁵(96-digit number)

19036182058043227628…10122608111047147521

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

3.807 × 10⁹⁵(96-digit number)

38072364116086455257…20245216222094295039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.807 × 10⁹⁵(96-digit number)

38072364116086455257…20245216222094295041

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

7.614 × 10⁹⁵(96-digit number)

76144728232172910515…40490432444188590079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.614 × 10⁹⁵(96-digit number)

76144728232172910515…40490432444188590081

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

1.522 × 10⁹⁶(97-digit number)

15228945646434582103…80980864888377180159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.522 × 10⁹⁶(97-digit number)

15228945646434582103…80980864888377180161

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

3.045 × 10⁹⁶(97-digit number)

30457891292869164206…61961729776754360319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.045 × 10⁹⁶(97-digit number)

30457891292869164206…61961729776754360321

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 #2,068,938

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