Block #207,378

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 10:04:20 AM · Difficulty 9.9025 · 6,618,179 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23ee1d399bd81102ede05fe0a111a185b064cd6af67020bf7edb05d4910b2fba

View on Chainz ↗

Height

#207,378

Difficulty

9.902470

Transactions

Size

199 B

Version

Bits

09e70844

Nonce

209,332

Timestamp

10/13/2013, 10:04:20 AM

Confirmations

6,618,179

Mined by

⛏️ P2SHAK7kWkL4sngiZYayFhX74gnWY2GHfWFBHC

Merkle Root

418875d76888ef4649c1a93073d89726304d993ab060cde603f693efb7704642

Transactions (1)

Coinbase418875d76888ef…f693efb7704642

1 in → 1 out10.1800 XPM109 B

AK7kWkL4…GHfWFBHC

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.

3.272 × 10⁹⁵(96-digit number)

32727697609604677154…39069850186421438039

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

3.272 × 10⁹⁵(96-digit number)

32727697609604677154…39069850186421438039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.272 × 10⁹⁵(96-digit number)

32727697609604677154…39069850186421438041

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

6.545 × 10⁹⁵(96-digit number)

65455395219209354308…78139700372842876079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.545 × 10⁹⁵(96-digit number)

65455395219209354308…78139700372842876081

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

1.309 × 10⁹⁶(97-digit number)

13091079043841870861…56279400745685752159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.309 × 10⁹⁶(97-digit number)

13091079043841870861…56279400745685752161

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

2.618 × 10⁹⁶(97-digit number)

26182158087683741723…12558801491371504319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.618 × 10⁹⁶(97-digit number)

26182158087683741723…12558801491371504321

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

5.236 × 10⁹⁶(97-digit number)

52364316175367483447…25117602982743008639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.236 × 10⁹⁶(97-digit number)

52364316175367483447…25117602982743008641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #207,378

Cookie Preferences