Block #2,111,592

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2017, 1:54:57 PM · Difficulty 10.9028 · 4,727,204 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1e696a56a9b386ddc050b8fafbe0846e986a1cb05a5d36b7d19b317090b549c7

View on Chainz ↗

Height

#2,111,592

Difficulty

10.902842

Transactions

Size

1.15 KB

Version

Bits

0ae720a5

Nonce

650,326,595

Timestamp

5/11/2017, 1:54:57 PM

Confirmations

4,727,204

Mined by

⛏️ P2SHANHhNqDP3y1rPUTYyvFTj3qsqSiDorGWV3

Merkle Root

d3b0aba2fb28098b98ba4fec16b75348953e71b13dd90d42aec241142a7abb70

Transactions (4)

Coinbaseed9be1928def61…11c8db2a3bf3c6

1 in → 1 out8.4300 XPM109 B

ANHhNqDP…iDorGWV3

114486558c706b…c64d3d5c2f8378

1 in → 2 out162586.5948 XPM226 B

AcCAcWBb…DVnSk8mK AQ61jELa…6LqTckJ2

3503bc5c630367…ab344b3861b58f

3 in → 2 out2089.7054 XPM524 B

AXJWN3KB…bTLm6xZn AKQJUnwV…mgLMEfah

e422552dc17677…59b6ae31d8647d

1 in → 2 out161512.0388 XPM226 B

AYF9LzVW…ruhWvC4M AUfiNpNR…r4iERJXe

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.

2.276 × 10⁹⁸(99-digit number)

22767551868850575458…21450595272114503679

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

2.276 × 10⁹⁸(99-digit number)

22767551868850575458…21450595272114503679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.276 × 10⁹⁸(99-digit number)

22767551868850575458…21450595272114503681

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

4.553 × 10⁹⁸(99-digit number)

45535103737701150916…42901190544229007359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.553 × 10⁹⁸(99-digit number)

45535103737701150916…42901190544229007361

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

9.107 × 10⁹⁸(99-digit number)

91070207475402301833…85802381088458014719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.107 × 10⁹⁸(99-digit number)

91070207475402301833…85802381088458014721

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

1.821 × 10⁹⁹(100-digit number)

18214041495080460366…71604762176916029439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.821 × 10⁹⁹(100-digit number)

18214041495080460366…71604762176916029441

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

3.642 × 10⁹⁹(100-digit number)

36428082990160920733…43209524353832058879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.642 × 10⁹⁹(100-digit number)

36428082990160920733…43209524353832058881

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 #2,111,592

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