Block #242,275

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 4:07:25 PM · Difficulty 9.9595 · 6,552,599 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e0332bd00305b01764a07257749b50e6888404c4117506f1b8d1e86db0ab56c

View on Chainz ↗

Height

#242,275

Difficulty

9.959494

Transactions

Size

576 B

Version

Bits

09f5a164

Nonce

30,757

Timestamp

11/3/2013, 4:07:25 PM

Confirmations

6,552,599

Mined by

⛏️ P2SHAXkwZGZQUV996sgzkcs2jbamXUaP3jC9dV

Merkle Root

3c0a4cca33722897436afac2d74ad91757aeac3ec0d33d57779bfdcf60db5241

Transactions (2)

Coinbaseefd3535b7f5e4d…0502de2575d0ce

1 in → 1 out10.0800 XPM109 B

AXkwZGZQ…aP3jC9dV

947d0efd23aae5…9c8303e322f26a

2 in → 2 out500.0101 XPM374 B

AVjHrsJJ…8LNnoxm7 ASzB7F59…9VwK4HYR

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.

4.846 × 10¹⁰¹(102-digit number)

48461919014170801026…66278715295458421279

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

4.846 × 10¹⁰¹(102-digit number)

48461919014170801026…66278715295458421279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.846 × 10¹⁰¹(102-digit number)

48461919014170801026…66278715295458421281

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

9.692 × 10¹⁰¹(102-digit number)

96923838028341602053…32557430590916842559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.692 × 10¹⁰¹(102-digit number)

96923838028341602053…32557430590916842561

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

1.938 × 10¹⁰²(103-digit number)

19384767605668320410…65114861181833685119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.938 × 10¹⁰²(103-digit number)

19384767605668320410…65114861181833685121

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

3.876 × 10¹⁰²(103-digit number)

38769535211336640821…30229722363667370239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.876 × 10¹⁰²(103-digit number)

38769535211336640821…30229722363667370241

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

7.753 × 10¹⁰²(103-digit number)

77539070422673281642…60459444727334740479

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