Block #94,243

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/2/2013, 11:14:02 PM · Difficulty 9.2027 · 6,705,085 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96ef1211121a3cc2e8eeebcedd4bb12d53dfb733a3b5d025d7fd332956ddb209

View on Chainz ↗

Height

#94,243

Difficulty

9.202682

Transactions

Size

206 B

Version

Bits

0933e2fd

Nonce

60,841

Timestamp

8/2/2013, 11:14:02 PM

Confirmations

6,705,085

Mined by

⛏️ P2SHAcBadmkptMo3EwP8cg9ZUyqvJMGmhL921o

Merkle Root

412950db1495ffca8dd3e2018439143ef13ae0d1462db2f6ec5c1f21b8c13099

Transactions (1)

Coinbase412950db1495ff…5c1f21b8c13099

1 in → 1 out11.7900 XPM109 B

AcBadmkp…GmhL921o

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.

1.140 × 10¹¹²(113-digit number)

11403749935380967571…41442925377202833529

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

1.140 × 10¹¹²(113-digit number)

11403749935380967571…41442925377202833529

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.140 × 10¹¹²(113-digit number)

11403749935380967571…41442925377202833531

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

2.280 × 10¹¹²(113-digit number)

22807499870761935143…82885850754405667059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.280 × 10¹¹²(113-digit number)

22807499870761935143…82885850754405667061

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

4.561 × 10¹¹²(113-digit number)

45614999741523870286…65771701508811334119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.561 × 10¹¹²(113-digit number)

45614999741523870286…65771701508811334121

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

9.122 × 10¹¹²(113-digit number)

91229999483047740573…31543403017622668239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.122 × 10¹¹²(113-digit number)

91229999483047740573…31543403017622668241

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

1.824 × 10¹¹³(114-digit number)

18245999896609548114…63086806035245336479

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