Block #1,756,853

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/10/2016, 6:24:20 PM · Difficulty 10.7150 · 5,052,525 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7e9e8030e5c27329c034258b45ddfc0842308b9062aca23a8137913b9ee04f3

View on Chainz ↗

Height

#1,756,853

Difficulty

10.715022

Transactions

Size

3.89 KB

Version

Bits

0ab70bb5

Nonce

76,437,434

Timestamp

9/10/2016, 6:24:20 PM

Confirmations

5,052,525

Mined by

⛏️ P2SHATwQiEy9QPv5bVP55xhJi7rC4CT7W4Xi9m

Merkle Root

8335d1caa3c4ac8d848fac2d4bed07594e0288dc7c3bf1819abbe8bef6172adf

Transactions (3)

Coinbase50efb7bfeab0ed…a8ce39f9b8df5f

1 in → 1 out8.7400 XPM109 B

ATwQiEy9…T7W4Xi9m

3156248f9fe901…438385b2c89f67

1 in → 51 out127.8778 XPM1.85 KB

AXyBuVut…5GTtjsrs ANiTFZMA…ufBYqC23 ASLXSjjt…roLfiETt ATwGZZAS…jtb9cEYm ASWw5hsH…2obnujqX

582606a73bd248…0e3c77210fba06

1 in → 51 out40.8637 XPM1.85 KB

AUJ8yWMj…xhRnTpAf ANNMAvtF…mEXi7Pgg AURirRbd…94jeeiPT Af2M2b1e…QUYoHpRx Adn6K5UG…3gkw6BeU

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.

1.322 × 10⁹⁴(95-digit number)

13225024038631932931…50851620624854377389

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

1.322 × 10⁹⁴(95-digit number)

13225024038631932931…50851620624854377389

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.322 × 10⁹⁴(95-digit number)

13225024038631932931…50851620624854377391

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

2.645 × 10⁹⁴(95-digit number)

26450048077263865862…01703241249708754779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.645 × 10⁹⁴(95-digit number)

26450048077263865862…01703241249708754781

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

5.290 × 10⁹⁴(95-digit number)

52900096154527731725…03406482499417509559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.290 × 10⁹⁴(95-digit number)

52900096154527731725…03406482499417509561

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

1.058 × 10⁹⁵(96-digit number)

10580019230905546345…06812964998835019119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.058 × 10⁹⁵(96-digit number)

10580019230905546345…06812964998835019121

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

2.116 × 10⁹⁵(96-digit number)

21160038461811092690…13625929997670038239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.116 × 10⁹⁵(96-digit number)

21160038461811092690…13625929997670038241

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 #1,756,853

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