Block #242,236

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 3:42:19 PM · Difficulty 9.9594 · 6,572,886 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c3760cd0c1199f6f5b86fbc9481cef6cd568468ae8d9fd525678df05d0a3738

View on Chainz ↗

Height

#242,236

Difficulty

9.959366

Transactions

Size

841 B

Version

Bits

09f59901

Nonce

12,945

Timestamp

11/3/2013, 3:42:19 PM

Confirmations

6,572,886

Mined by

⛏️ P2SHAKGPMtXTr4JyvYebuAsZG5zXUn2hcKyhCH

Merkle Root

1e124fbea2d01ff8416933eb1fc8c5c1f853561e07b6b7be1d9ef101d327f6d6

Transactions (4)

Coinbase50b4d0e93e7f89…f80b55bc4cd485

1 in → 1 out10.1000 XPM109 B

AKGPMtXT…2hcKyhCH

1a87a3e628b70d…229158c410ba1b

1 in → 2 out131.5315 XPM225 B

AMVWyjLP…hcqYAvaF AZdmkNt9…Dk8ffFeU

65f3285cc48ef6…c652d3b756d33d

1 in → 2 out124.7808 XPM225 B

AJFxAB9V…eD9UQC2e ATknEwpv…tz6xvy1e

b22d477ec7c5fa…7c7d5517abed22

1 in → 1 out123.7708 XPM192 B

ATknEwpv…tz6xvy1e

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.

7.127 × 10⁹³(94-digit number)

71270267121002314211…30313180671952699599

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

7.127 × 10⁹³(94-digit number)

71270267121002314211…30313180671952699599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.127 × 10⁹³(94-digit number)

71270267121002314211…30313180671952699601

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

1.425 × 10⁹⁴(95-digit number)

14254053424200462842…60626361343905399199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.425 × 10⁹⁴(95-digit number)

14254053424200462842…60626361343905399201

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

2.850 × 10⁹⁴(95-digit number)

28508106848400925684…21252722687810798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.850 × 10⁹⁴(95-digit number)

28508106848400925684…21252722687810798401

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

5.701 × 10⁹⁴(95-digit number)

57016213696801851369…42505445375621596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.701 × 10⁹⁴(95-digit number)

57016213696801851369…42505445375621596801

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

1.140 × 10⁹⁵(96-digit number)

11403242739360370273…85010890751243193599

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 #242,236

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