Block #814,254

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/16/2014, 9:39:31 PM · Difficulty 10.9739 · 6,002,871 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3fec936294de4ccaff4f59beba71b0febe91af50623c572eca7cace845a0c563

View on Chainz ↗

Height

#814,254

Difficulty

10.973922

Transactions

Size

244 B

Version

Bits

0af952ef

Nonce

522,567,545

Timestamp

11/16/2014, 9:39:31 PM

Confirmations

6,002,871

Mined by

⛏️ P2SHAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

ca780432aa45d8b055ad884ca6eedac66671d8814a75ce035747eff3fe5cef7c

Transactions (1)

Coinbaseca780432aa45d8…47eff3fe5cef7c

1 in → 2 out8.2900 XPM152 B

AYFivgcJ…FT8wELGF ALPu3s2c…EJXLjVFh

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.

2.299 × 10⁹⁹(100-digit number)

22997510489708702438…18268676602311147519

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

2.299 × 10⁹⁹(100-digit number)

22997510489708702438…18268676602311147519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.299 × 10⁹⁹(100-digit number)

22997510489708702438…18268676602311147521

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

4.599 × 10⁹⁹(100-digit number)

45995020979417404876…36537353204622295039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.599 × 10⁹⁹(100-digit number)

45995020979417404876…36537353204622295041

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

9.199 × 10⁹⁹(100-digit number)

91990041958834809753…73074706409244590079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.199 × 10⁹⁹(100-digit number)

91990041958834809753…73074706409244590081

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

1.839 × 10¹⁰⁰(101-digit number)

18398008391766961950…46149412818489180159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.839 × 10¹⁰⁰(101-digit number)

18398008391766961950…46149412818489180161

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

3.679 × 10¹⁰⁰(101-digit number)

36796016783533923901…92298825636978360319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.679 × 10¹⁰⁰(101-digit number)

36796016783533923901…92298825636978360321

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 #814,254

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