Block #1,682,109

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/20/2016, 6:55:04 PM · Difficulty 10.7185 · 5,148,438 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4fd9443a2d4638b691e314d1007ae3443ae2279670a59d8c212814375e91419

View on Chainz ↗

Height

#1,682,109

Difficulty

10.718534

Transactions

Size

1016 B

Version

Bits

0ab7f1d6

Nonce

1,439,937,375

Timestamp

7/20/2016, 6:55:04 PM

Confirmations

5,148,438

Mined by

⛏️ P2SHATrzJ5Cg2H2BD1AgfhyAGGW9SxEPkdHYg7

Merkle Root

d0b1123ece5d97b6d97e0729525c338bd5907be4de8bd8db1208934c9861946f

Transactions (2)

Coinbase0c65f12967e313…f8a3eb94faf1e5

1 in → 1 out8.7000 XPM109 B

ATrzJ5Cg…EPkdHYg7

ba5ee09842b0f2…6e41a710f9153e

5 in → 2 out51.3300 XPM817 B

AQcjeddP…AoqhXrhG AarvMAYA…ajqL51BZ

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.

4.189 × 10⁹⁴(95-digit number)

41896053293648944742…26339364129284577279

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

4.189 × 10⁹⁴(95-digit number)

41896053293648944742…26339364129284577279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.189 × 10⁹⁴(95-digit number)

41896053293648944742…26339364129284577281

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

8.379 × 10⁹⁴(95-digit number)

83792106587297889484…52678728258569154559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.379 × 10⁹⁴(95-digit number)

83792106587297889484…52678728258569154561

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

1.675 × 10⁹⁵(96-digit number)

16758421317459577896…05357456517138309119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.675 × 10⁹⁵(96-digit number)

16758421317459577896…05357456517138309121

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

3.351 × 10⁹⁵(96-digit number)

33516842634919155793…10714913034276618239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.351 × 10⁹⁵(96-digit number)

33516842634919155793…10714913034276618241

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

6.703 × 10⁹⁵(96-digit number)

67033685269838311587…21429826068553236479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.703 × 10⁹⁵(96-digit number)

67033685269838311587…21429826068553236481

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 #1,682,109

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