Block #41,145

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:09:39 PM · Difficulty 8.4990 · 6,749,845 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ab7ba6e6adb576f2d9875dfbf56b5255e30b0999bf6bc31a67e5a448b90ca4f

View on Chainz ↗

Height

#41,145

Difficulty

8.499026

Transactions

Size

632 B

Version

Bits

087fc029

Nonce

187

Timestamp

7/14/2013, 4:09:39 PM

Confirmations

6,749,845

Merkle Root

d71bf84d0357cd7270738a89ff4fbf0b7b947cf01cd089c49c9062abddd1eec2

Transactions (3)

Coinbase484febf29aaea9…8a5cf5ee118015

1 in → 1 out13.8500 XPM110 B

Aeg73xq9…k2T5gw66

e297526d7affa0…354645f2b37d1c

2 in → 1 out31.2700 XPM271 B

AG43TCYA…UW1AUz7e

9c1256eb5bbbd5…2ebca116051bca

1 in → 1 out15.6200 XPM158 B

AJV9J7t5…G9F5PrK8

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.

1.422 × 10¹⁰²(103-digit number)

14229808598092256133…40283744286918969959

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

1.422 × 10¹⁰²(103-digit number)

14229808598092256133…40283744286918969959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.422 × 10¹⁰²(103-digit number)

14229808598092256133…40283744286918969961

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

2.845 × 10¹⁰²(103-digit number)

28459617196184512266…80567488573837939919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.845 × 10¹⁰²(103-digit number)

28459617196184512266…80567488573837939921

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

5.691 × 10¹⁰²(103-digit number)

56919234392369024533…61134977147675879839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.691 × 10¹⁰²(103-digit number)

56919234392369024533…61134977147675879841

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

1.138 × 10¹⁰³(104-digit number)

11383846878473804906…22269954295351759679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.138 × 10¹⁰³(104-digit number)

11383846878473804906…22269954295351759681

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