Block #243,226

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 4:25:38 AM · Difficulty 9.9612 · 6,551,626 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

af7872608e7e3fafc5c83387022decb51030cbb2dca27fe90a6b2f8093edfcaa

View on Chainz ↗

Height

#243,226

Difficulty

9.961194

Transactions

Size

721 B

Version

Bits

09f610d4

Nonce

13,006

Timestamp

11/4/2013, 4:25:38 AM

Confirmations

6,551,626

Mined by

⛏️ P2SHAXbpyooSXrgsDVAsu6AkhX5vgBbup7bQTH

Merkle Root

557159efa9c16581bc0712a722600d255bed7ea172e37f2efb251d016b55cba9

Transactions (2)

Coinbase02db66b71011f6…ac26ae83f74ed9

1 in → 1 out10.0700 XPM109 B

AXbpyooS…bup7bQTH

24a6b0838f21e3…b0773528997167

3 in → 2 out2.0650 XPM523 B

AXyv8ehd…YyjxK2yi AWAbscvz…vDzdxS8b

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.

1.925 × 10⁹³(94-digit number)

19253548684550186572…00543642117780898879

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

1.925 × 10⁹³(94-digit number)

19253548684550186572…00543642117780898879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.925 × 10⁹³(94-digit number)

19253548684550186572…00543642117780898881

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

3.850 × 10⁹³(94-digit number)

38507097369100373145…01087284235561797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.850 × 10⁹³(94-digit number)

38507097369100373145…01087284235561797761

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

7.701 × 10⁹³(94-digit number)

77014194738200746290…02174568471123595519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.701 × 10⁹³(94-digit number)

77014194738200746290…02174568471123595521

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

1.540 × 10⁹⁴(95-digit number)

15402838947640149258…04349136942247191039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.540 × 10⁹⁴(95-digit number)

15402838947640149258…04349136942247191041

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

3.080 × 10⁹⁴(95-digit number)

30805677895280298516…08698273884494382079

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