Block #41,146

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:09:45 PM · Difficulty 8.4991 · 6,750,617 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b1a1a84df78a897a83c1fba25b07d11384dde85cea148be20a4d3c1226ff0672

View on Chainz ↗

Height

#41,146

Difficulty

8.499112

Transactions

Size

198 B

Version

Bits

087fc5cf

Nonce

294

Timestamp

7/14/2013, 4:09:45 PM

Confirmations

6,750,617

Merkle Root

aeebbce0348c8c8984e79dc3b7daee6f3a000935ca7e12cb8ce802ed33e9b624

Transactions (1)

Coinbaseaeebbce0348c8c…e802ed33e9b624

1 in → 1 out13.8200 XPM110 B

ANCYL9xh…9WyGnqDE

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.

6.253 × 10⁸⁸(89-digit number)

62534989801074149851…01059914107199311299

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

6.253 × 10⁸⁸(89-digit number)

62534989801074149851…01059914107199311299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.253 × 10⁸⁸(89-digit number)

62534989801074149851…01059914107199311301

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

1.250 × 10⁸⁹(90-digit number)

12506997960214829970…02119828214398622599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.250 × 10⁸⁹(90-digit number)

12506997960214829970…02119828214398622601

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

2.501 × 10⁸⁹(90-digit number)

25013995920429659940…04239656428797245199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.501 × 10⁸⁹(90-digit number)

25013995920429659940…04239656428797245201

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

5.002 × 10⁸⁹(90-digit number)

50027991840859319881…08479312857594490399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.002 × 10⁸⁹(90-digit number)

50027991840859319881…08479312857594490401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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