Block #1,197,131

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/17/2015, 12:57:05 AM · Difficulty 10.8262 · 5,616,923 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00c72e0155a66753caf01c9ff0c097f092315b6f233fcbd0b97856ff22a2c74b

View on Chainz ↗

Height

#1,197,131

Difficulty

10.826237

Transactions

Size

3.30 KB

Version

Bits

0ad3844d

Nonce

57,719,578

Timestamp

8/17/2015, 12:57:05 AM

Confirmations

5,616,923

Mined by

⛏️ P2SHAGzGqQr6vTNiEpue9CZV6YQSanwKDqKeyz

Merkle Root

be242742b7dcf685667b188b23f51c3c7e354b5236fc4147fe863c07c0789327

Transactions (2)

Coinbase15f61356aee9a0…484ba426438909

1 in → 1 out8.5600 XPM109 B

AGzGqQr6…wKDqKeyz

e52a2c9c8cac28…696c210e092a36

21 in → 2 out220.7227 XPM3.11 KB

ALMSQgRT…mxrxK7kX AJVeRHXf…C2yREH1f

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.

4.497 × 10⁹⁴(95-digit number)

44976457539456564922…51949188617572711519

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

4.497 × 10⁹⁴(95-digit number)

44976457539456564922…51949188617572711519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.497 × 10⁹⁴(95-digit number)

44976457539456564922…51949188617572711521

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

8.995 × 10⁹⁴(95-digit number)

89952915078913129845…03898377235145423039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.995 × 10⁹⁴(95-digit number)

89952915078913129845…03898377235145423041

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

1.799 × 10⁹⁵(96-digit number)

17990583015782625969…07796754470290846079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.799 × 10⁹⁵(96-digit number)

17990583015782625969…07796754470290846081

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

3.598 × 10⁹⁵(96-digit number)

35981166031565251938…15593508940581692159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.598 × 10⁹⁵(96-digit number)

35981166031565251938…15593508940581692161

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

7.196 × 10⁹⁵(96-digit number)

71962332063130503876…31187017881163384319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.196 × 10⁹⁵(96-digit number)

71962332063130503876…31187017881163384321

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 #1,197,131

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