Block #41,486

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:44:05 PM · Difficulty 8.5286 · 6,755,326 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7fc131290361804ce9f5b89bd72f447d254fefdeb03dd500145a18ffa72e0ec7

View on Chainz ↗

Height

#41,486

Difficulty

8.528607

Transactions

Size

469 B

Version

Bits

088752cf

Nonce

830

Timestamp

7/14/2013, 4:44:05 PM

Confirmations

6,755,326

Mined by

⛏️ P2SHAbYdBKJD6PA9JLndgBE5DDh2iQoAUbyk4B

Merkle Root

cf79b4b646c12ba0e6f78121c19e32ab53d29a892cbbef257b09e5971cc1fced

Transactions (2)

Coinbase1fda25728876d4…34fe7431d0e830

1 in → 1 out13.7400 XPM110 B

AbYdBKJD…oAUbyk4B

6e74d455ffceac…e3f8bb0ddb9f34

2 in → 1 out31.2500 XPM271 B

Ad1eJZGM…SrcXNe7U

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.

2.398 × 10⁸⁹(90-digit number)

23981573227347816803…79560572457491115189

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

2.398 × 10⁸⁹(90-digit number)

23981573227347816803…79560572457491115189

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.398 × 10⁸⁹(90-digit number)

23981573227347816803…79560572457491115191

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

4.796 × 10⁸⁹(90-digit number)

47963146454695633607…59121144914982230379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.796 × 10⁸⁹(90-digit number)

47963146454695633607…59121144914982230381

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

9.592 × 10⁸⁹(90-digit number)

95926292909391267215…18242289829964460759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.592 × 10⁸⁹(90-digit number)

95926292909391267215…18242289829964460761

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

1.918 × 10⁹⁰(91-digit number)

19185258581878253443…36484579659928921519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.918 × 10⁹⁰(91-digit number)

19185258581878253443…36484579659928921521

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