Block #205,370

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 2:53:41 AM · Difficulty 9.8997 · 6,588,800 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c6b82875fe83f88bf780e4e066ff4e0c0a8eeb66b75b9fc2784f5c4056514700

View on Chainz ↗

Height

#205,370

Difficulty

9.899655

Transactions

Size

650 B

Version

Bits

09e64fcd

Nonce

17,494

Timestamp

10/12/2013, 2:53:41 AM

Confirmations

6,588,800

Merkle Root

88ed545846a609299cc40148cfa03430ffc68edf4f7bf1efb513d103d6b1c0c7

Transactions (3)

Coinbase83868b480a11fa…8cf43bcd06ae90

1 in → 1 out10.2100 XPM109 B

ATPMUVRY…YtxTHDNH

74b5469fc15e6c…13ee535d5ffd59

1 in → 2 out10.1900 XPM226 B

AdUodsdP…yVn57E7G AQZrJXfv…m8Y2mX47

988642fe960a9b…b3d9adc9d972d7

1 in → 2 out8.1405 XPM225 B

AVYA5FSq…eeZm8KGY AH42ooyR…cb6QuM5K

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.

9.327 × 10⁹³(94-digit number)

93272081987041335498…63828073805702828999

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

9.327 × 10⁹³(94-digit number)

93272081987041335498…63828073805702828999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.327 × 10⁹³(94-digit number)

93272081987041335498…63828073805702829001

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

1.865 × 10⁹⁴(95-digit number)

18654416397408267099…27656147611405657999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.865 × 10⁹⁴(95-digit number)

18654416397408267099…27656147611405658001

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

3.730 × 10⁹⁴(95-digit number)

37308832794816534199…55312295222811315999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.730 × 10⁹⁴(95-digit number)

37308832794816534199…55312295222811316001

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

7.461 × 10⁹⁴(95-digit number)

74617665589633068398…10624590445622631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.461 × 10⁹⁴(95-digit number)

74617665589633068398…10624590445622632001

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

1.492 × 10⁹⁵(96-digit number)

14923533117926613679…21249180891245263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.492 × 10⁹⁵(96-digit number)

14923533117926613679…21249180891245264001

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