Block #2,261,682

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/21/2017, 1:25:05 PM · Difficulty 10.9523 · 4,570,071 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32cb17558b4be773cab44ea383ff2a21a6edba547dce2792b4ff36c65838aabb

View on Chainz ↗

Height

#2,261,682

Difficulty

10.952341

Transactions

Size

869 B

Version

Bits

0af3cca1

Nonce

36,740,624

Timestamp

8/21/2017, 1:25:05 PM

Confirmations

4,570,071

Mined by

⛏️ P2SHATWVgjwcPeqdVNZ14WAoR4VVGZpFvTZzAC

Merkle Root

f7230bf53a1891fa8923c21d5ccb9c03799d5a7a090de9a6b7b74f67cef5a54c

Transactions (2)

Coinbasea37a9735bc7eb1…2a5522500ab5b4

1 in → 1 out8.3300 XPM109 B

ATWVgjwc…pFvTZzAC

3e532654cf754a…ed7d807e91910a

4 in → 2 out1483.0472 XPM670 B

AZGStUHo…ii1maJpV AagZTgTw…8sDcTvr3

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.

2.269 × 10⁹⁴(95-digit number)

22699088108135652743…32658109074875248119

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

2.269 × 10⁹⁴(95-digit number)

22699088108135652743…32658109074875248119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.269 × 10⁹⁴(95-digit number)

22699088108135652743…32658109074875248121

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

4.539 × 10⁹⁴(95-digit number)

45398176216271305486…65316218149750496239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.539 × 10⁹⁴(95-digit number)

45398176216271305486…65316218149750496241

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

9.079 × 10⁹⁴(95-digit number)

90796352432542610973…30632436299500992479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.079 × 10⁹⁴(95-digit number)

90796352432542610973…30632436299500992481

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

1.815 × 10⁹⁵(96-digit number)

18159270486508522194…61264872599001984959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.815 × 10⁹⁵(96-digit number)

18159270486508522194…61264872599001984961

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

3.631 × 10⁹⁵(96-digit number)

36318540973017044389…22529745198003969919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.631 × 10⁹⁵(96-digit number)

36318540973017044389…22529745198003969921

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 #2,261,682

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