Block #41,490

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 4:44:42 PM · Difficulty 8.5289 · 6,747,913 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

57d0ddb06910752328786792c347034d565c98ac876cb5571d5836c693e5d854

View on Chainz ↗

Height

#41,490

Difficulty

8.528911

Transactions

Size

2.24 KB

Version

Bits

088766bc

Nonce

Timestamp

7/14/2013, 4:44:42 PM

Confirmations

6,747,913

Merkle Root

59a43223bc05d5e7ef0a019b7b1d01c7cb4e4134ae876c88caa5e62ce9596a2f

Transactions (2)

Coinbasecc6bff4f112019…be086933f1743a

1 in → 1 out13.7600 XPM110 B

AWUvjqWF…XhwuTcBE

835e10a399fe63…2d11c3988af3e5

18 in → 1 out296.3900 XPM2.04 KB

AFn4u75n…2Yn1dYNc

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.

3.399 × 10¹⁰⁵(106-digit number)

33993843300500657586…18249470143583574439

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

3.399 × 10¹⁰⁵(106-digit number)

33993843300500657586…18249470143583574439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.399 × 10¹⁰⁵(106-digit number)

33993843300500657586…18249470143583574441

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

6.798 × 10¹⁰⁵(106-digit number)

67987686601001315173…36498940287167148879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.798 × 10¹⁰⁵(106-digit number)

67987686601001315173…36498940287167148881

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

1.359 × 10¹⁰⁶(107-digit number)

13597537320200263034…72997880574334297759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.359 × 10¹⁰⁶(107-digit number)

13597537320200263034…72997880574334297761

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

2.719 × 10¹⁰⁶(107-digit number)

27195074640400526069…45995761148668595519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.719 × 10¹⁰⁶(107-digit number)

27195074640400526069…45995761148668595521

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