Block #2,294,120

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/13/2017, 2:20:09 AM · Difficulty 10.9532 · 4,537,392 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a80bb63ede11d42eb593da229c220dd79e604e18e1307dd87684b229b0fc5bca

View on Chainz ↗

Height

#2,294,120

Difficulty

10.953200

Transactions

Size

650 B

Version

Bits

0af404e7

Nonce

405,847,084

Timestamp

9/13/2017, 2:20:09 AM

Confirmations

4,537,392

Mined by

⛏️ P2SHAdHxVCbHPpVNFUKPyZqLEvUNfo8FdzcMkb

Merkle Root

3c6bbc47146996c7ec09754376991d4e5b6f24533fcc76f8b7d39b6f997e8ee8

Transactions (3)

Coinbase84870688ed3be7…ecf78cc7a1f728

1 in → 1 out8.3400 XPM110 B

AdHxVCbH…8FdzcMkb

d11bdebdc51492…afe63e497c2aca

1 in → 2 out6343.9056 XPM225 B

Ac5R2GzM…bTYYawaJ AQSrJg2m…iPfiNZ9k

455d8f6b028d2d…dfbe78400bbde0

1 in → 2 out282.2797 XPM225 B

AdeAPFMZ…K4yZks7e ASscYTgZ…VxRvC6Nd

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.

1.021 × 10⁹⁵(96-digit number)

10219264624661426051…49462448854996776079

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

1.021 × 10⁹⁵(96-digit number)

10219264624661426051…49462448854996776079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.021 × 10⁹⁵(96-digit number)

10219264624661426051…49462448854996776081

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

2.043 × 10⁹⁵(96-digit number)

20438529249322852103…98924897709993552159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.043 × 10⁹⁵(96-digit number)

20438529249322852103…98924897709993552161

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

4.087 × 10⁹⁵(96-digit number)

40877058498645704207…97849795419987104319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.087 × 10⁹⁵(96-digit number)

40877058498645704207…97849795419987104321

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

8.175 × 10⁹⁵(96-digit number)

81754116997291408415…95699590839974208639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.175 × 10⁹⁵(96-digit number)

81754116997291408415…95699590839974208641

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

1.635 × 10⁹⁶(97-digit number)

16350823399458281683…91399181679948417279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.635 × 10⁹⁶(97-digit number)

16350823399458281683…91399181679948417281

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 #2,294,120

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