Block #243,185

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 3:55:13 AM · Difficulty 9.9611 · 6,570,696 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2f9fb1307106daf37c2e0606a9a7bc2cb392f08cd0137496f67a77c9e9888b45

View on Chainz ↗

Height

#243,185

Difficulty

9.961110

Transactions

Size

458 B

Version

Bits

09f60b4e

Nonce

36,291

Timestamp

11/4/2013, 3:55:13 AM

Confirmations

6,570,696

Mined by

⛏️ P2SHARpjo1R1CW6469WP7jPxmTMQ4pYjsCmHPk

Merkle Root

3943abfcff660c5fbf72e1ddfc1bea5650f3381d93e9821c05561b24b145699a

Transactions (2)

Coinbase36c162b735254d…792873774bf6a6

1 in → 1 out10.0700 XPM109 B

ARpjo1R1…YjsCmHPk

28dcd0d394257f…af6b2696ab2b6a

1 in → 4 out10.0700 XPM259 B

AeKNrjNj…1NEq95Ta Af5JcoF1…bCtmmgeZ Ac5Wp7cR…cjU1uyVK ARTJCDz1…oJ6Hi1d9

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.

4.501 × 10⁹⁵(96-digit number)

45015244184580868693…94309461078717878079

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

4.501 × 10⁹⁵(96-digit number)

45015244184580868693…94309461078717878079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.501 × 10⁹⁵(96-digit number)

45015244184580868693…94309461078717878081

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

9.003 × 10⁹⁵(96-digit number)

90030488369161737386…88618922157435756159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.003 × 10⁹⁵(96-digit number)

90030488369161737386…88618922157435756161

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

1.800 × 10⁹⁶(97-digit number)

18006097673832347477…77237844314871512319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.800 × 10⁹⁶(97-digit number)

18006097673832347477…77237844314871512321

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

3.601 × 10⁹⁶(97-digit number)

36012195347664694954…54475688629743024639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.601 × 10⁹⁶(97-digit number)

36012195347664694954…54475688629743024641

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

7.202 × 10⁹⁶(97-digit number)

72024390695329389909…08951377259486049279

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 #243,185

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