Block #1,766,716

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/17/2016, 5:57:22 AM · Difficulty 10.7438 · 5,058,112 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60b64e32eef179a671ad527cdad34ca99e645c82a2b11f85efab85464f1e660c

View on Chainz ↗

Height

#1,766,716

Difficulty

10.743834

Transactions

Size

6.63 KB

Version

Bits

0abe6bec

Nonce

670,545,772

Timestamp

9/17/2016, 5:57:22 AM

Confirmations

5,058,112

Mined by

⛏️ P2SHAP8APdVC6obSyNtbSzgjt4AsapBPvXZ73n

Merkle Root

5f3349be9315d1d000d57c12274dfe212bda163bdf03c7938c1f938e01dc45e0

Transactions (2)

Coinbase44cddf9b143bbc…7d58e344a44d96

1 in → 1 out8.7200 XPM110 B

AP8APdVC…BPvXZ73n

db54f6cc07ad6e…d13304534ca60d

44 in → 2 out362.3930 XPM6.43 KB

ANRijrHk…NtomCTKh AdvLfhqF…YUuRFQZL

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.

2.746 × 10⁹⁸(99-digit number)

27465037600515644775…52811269920189808639

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

2.746 × 10⁹⁸(99-digit number)

27465037600515644775…52811269920189808639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.746 × 10⁹⁸(99-digit number)

27465037600515644775…52811269920189808641

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

5.493 × 10⁹⁸(99-digit number)

54930075201031289550…05622539840379617279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.493 × 10⁹⁸(99-digit number)

54930075201031289550…05622539840379617281

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

1.098 × 10⁹⁹(100-digit number)

10986015040206257910…11245079680759234559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.098 × 10⁹⁹(100-digit number)

10986015040206257910…11245079680759234561

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

2.197 × 10⁹⁹(100-digit number)

21972030080412515820…22490159361518469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.197 × 10⁹⁹(100-digit number)

21972030080412515820…22490159361518469121

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

4.394 × 10⁹⁹(100-digit number)

43944060160825031640…44980318723036938239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.394 × 10⁹⁹(100-digit number)

43944060160825031640…44980318723036938241

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 #1,766,716

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