Block #1,768,891

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/18/2016, 6:15:15 PM · Difficulty 10.7437 · 5,040,687 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c3a263aa4ac4e93953a89fb32be625bf55576bd52408a36d0837cb3e9ba0b28

View on Chainz ↗

Height

#1,768,891

Difficulty

10.743724

Transactions

Size

425 B

Version

Bits

0abe64b3

Nonce

35,447,389

Timestamp

9/18/2016, 6:15:15 PM

Confirmations

5,040,687

Mined by

⛏️ P2SHARz1uu4CWPKUTUBAVgxM6ffQFJ35Y86Xm7

Merkle Root

c36826ace78f56bce57ab5d173db9bba932dbb1c58314b1e11416d2961692c55

Transactions (2)

Coinbase7769baa0214b6a…6417387fe82a39

1 in → 1 out8.6600 XPM109 B

ARz1uu4C…35Y86Xm7

672fff913fd77c…c7e76b05a8f718

1 in → 2 out19999.9900 XPM226 B

Ae4Dh5MX…6RcES7z6 AU94Bxn9…LGdrtsoQ

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.

2.069 × 10⁹⁵(96-digit number)

20697319015442262962…21436267460186521599

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

2.069 × 10⁹⁵(96-digit number)

20697319015442262962…21436267460186521599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.069 × 10⁹⁵(96-digit number)

20697319015442262962…21436267460186521601

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

4.139 × 10⁹⁵(96-digit number)

41394638030884525925…42872534920373043199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.139 × 10⁹⁵(96-digit number)

41394638030884525925…42872534920373043201

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

8.278 × 10⁹⁵(96-digit number)

82789276061769051851…85745069840746086399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.278 × 10⁹⁵(96-digit number)

82789276061769051851…85745069840746086401

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

1.655 × 10⁹⁶(97-digit number)

16557855212353810370…71490139681492172799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.655 × 10⁹⁶(97-digit number)

16557855212353810370…71490139681492172801

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

3.311 × 10⁹⁶(97-digit number)

33115710424707620740…42980279362984345599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.311 × 10⁹⁶(97-digit number)

33115710424707620740…42980279362984345601

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 #1,768,891

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