Block #2,149,731

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/7/2017, 6:26:04 AM · Difficulty 10.8983 · 4,693,611 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe69fd821cf148cf1c02f493d103bf07eb1ffe77cdbc41e95a5b8dce02624839

View on Chainz ↗

Height

#2,149,731

Difficulty

10.898287

Transactions

Size

427 B

Version

Bits

0ae5f626

Nonce

100,427,143

Timestamp

6/7/2017, 6:26:04 AM

Confirmations

4,693,611

Mined by

⛏️ P2SHAWNJzoJ4nw9AcM8tV5qRSR541oikAvUrDk

Merkle Root

99aa73983fb29ea0bec3ffe596c9ecf5cc20c6e85992b81b42338f7c245de497

Transactions (2)

Coinbase9cb33145fc2213…07874718e3c63a

1 in → 1 out8.4200 XPM110 B

AWNJzoJ4…ikAvUrDk

986e562f719b5e…c7787744537f30

1 in → 2 out19.5412 XPM227 B

AWvwxTAg…oKG2msm4 Ab3LMQiL…W5xY6iHS

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.

1.775 × 10⁹⁵(96-digit number)

17754244419580880672…48788574822825983999

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

1.775 × 10⁹⁵(96-digit number)

17754244419580880672…48788574822825983999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.775 × 10⁹⁵(96-digit number)

17754244419580880672…48788574822825984001

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

3.550 × 10⁹⁵(96-digit number)

35508488839161761345…97577149645651967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.550 × 10⁹⁵(96-digit number)

35508488839161761345…97577149645651968001

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

7.101 × 10⁹⁵(96-digit number)

71016977678323522690…95154299291303935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.101 × 10⁹⁵(96-digit number)

71016977678323522690…95154299291303936001

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

1.420 × 10⁹⁶(97-digit number)

14203395535664704538…90308598582607871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.420 × 10⁹⁶(97-digit number)

14203395535664704538…90308598582607872001

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

2.840 × 10⁹⁶(97-digit number)

28406791071329409076…80617197165215743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.840 × 10⁹⁶(97-digit number)

28406791071329409076…80617197165215744001

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 #2,149,731

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