Block #241,811

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 10:17:51 AM · Difficulty 9.9585 · 6,601,010 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41be320fd935db96ce3eda4feacbf11f0420e69a33d187473e7226fc1e5d0aff

View on Chainz ↗

Height

#241,811

Difficulty

9.958531

Transactions

Size

1.36 KB

Version

Bits

09f5624c

Nonce

138,282

Timestamp

11/3/2013, 10:17:51 AM

Confirmations

6,601,010

Mined by

⛏️ P2SHAM1VNW6UCby3B6NiMh61qZzVqLf1PMfySe

Merkle Root

765bfa33f5be73e914b49615f5100a5812ed39de45ec488210bccd9da23d15b0

Transactions (3)

Coinbase6d9d51f9445632…c6e5d9d9e5b4e0

1 in → 1 out10.0900 XPM109 B

AM1VNW6U…f1PMfySe

ee1c1b9b33e901…9da09d9aa8652e

4 in → 2 out133.2374 XPM671 B

AN3nSmk1…cLziA14P AZdmkNt9…Dk8ffFeU

fb35d6f7475bfb…d9942f031bdc26

3 in → 2 out2.0524 XPM522 B

AZJdvPbz…K2YZec42 AXSXA825…fR3ugsiA

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.

5.812 × 10⁹³(94-digit number)

58129817143116030783…02287083459778565879

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

5.812 × 10⁹³(94-digit number)

58129817143116030783…02287083459778565879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.812 × 10⁹³(94-digit number)

58129817143116030783…02287083459778565881

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

1.162 × 10⁹⁴(95-digit number)

11625963428623206156…04574166919557131759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.162 × 10⁹⁴(95-digit number)

11625963428623206156…04574166919557131761

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

2.325 × 10⁹⁴(95-digit number)

23251926857246412313…09148333839114263519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.325 × 10⁹⁴(95-digit number)

23251926857246412313…09148333839114263521

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

4.650 × 10⁹⁴(95-digit number)

46503853714492824626…18296667678228527039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.650 × 10⁹⁴(95-digit number)

46503853714492824626…18296667678228527041

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

9.300 × 10⁹⁴(95-digit number)

93007707428985649253…36593335356457054079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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

Block #241,811

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