Block #802,043

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/8/2014, 1:52:23 AM · Difficulty 10.9760 · 5,989,483 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4db22ea8d8e8acaaedf2c7652e4a2e5287c365fa8e0adb887187d7cc206bfe87

View on Chainz ↗

Height

#802,043

Difficulty

10.976011

Transactions

Size

731 B

Version

Bits

0af9dbe1

Nonce

6,292,012

Timestamp

11/8/2014, 1:52:23 AM

Confirmations

5,989,483

Merkle Root

4f9c36bd8fc65f19336c4edd85c09d36fe6a84c19ccb8a34d01eedbf65a10403

Transactions (2)

Coinbase3cb88918294190…f6f5903e611679

1 in → 1 out8.3000 XPM116 B

ANSXnLY2…Sd25TjkD

b01f9af71289b0…3376a32583a909

3 in → 2 out130.6480 XPM524 B

AZwr8cXp…irYz5Ah8 AHSYuthm…8ZKze41E

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.

2.058 × 10⁹⁸(99-digit number)

20580314598943222110…82021207753942899199

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

2.058 × 10⁹⁸(99-digit number)

20580314598943222110…82021207753942899199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.058 × 10⁹⁸(99-digit number)

20580314598943222110…82021207753942899201

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

4.116 × 10⁹⁸(99-digit number)

41160629197886444220…64042415507885798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.116 × 10⁹⁸(99-digit number)

41160629197886444220…64042415507885798401

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

8.232 × 10⁹⁸(99-digit number)

82321258395772888440…28084831015771596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.232 × 10⁹⁸(99-digit number)

82321258395772888440…28084831015771596801

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

1.646 × 10⁹⁹(100-digit number)

16464251679154577688…56169662031543193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.646 × 10⁹⁹(100-digit number)

16464251679154577688…56169662031543193601

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

3.292 × 10⁹⁹(100-digit number)

32928503358309155376…12339324063086387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.292 × 10⁹⁹(100-digit number)

32928503358309155376…12339324063086387201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.585 × 10⁹⁹(100-digit number)

65857006716618310752…24678648126172774399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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