Block #192,553

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 11:03:48 PM · Difficulty 9.8745 · 6,617,076 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1153379f8d8c24344971f8e311828cd3db664b7458cfa322eab28312a6158f98

View on Chainz ↗

Height

#192,553

Difficulty

9.874546

Transactions

Size

799 B

Version

Bits

09dfe240

Nonce

186,975

Timestamp

10/3/2013, 11:03:48 PM

Confirmations

6,617,076

Mined by

⛏️ P2SHAGPbvroz9hinzW2z7rW2tDLw79oN3HrusU

Merkle Root

f26643dd80e29d0e53ad9ecc67a7d2444555a1d41f3a3047f334e46a38239942

Transactions (3)

Coinbasebe7141bba72bed…1e024f212ae711

1 in → 1 out10.2600 XPM109 B

AGPbvroz…oN3HrusU

a1ce543bb0f58f…52c4c43ef05679

2 in → 2 out16.4114 XPM373 B

ALpthvGg…D1g5z4CT AdZWByYz…v6KaC6d5

cbac3033fff3af…0571ec9403db17

1 in → 2 out5.2586 XPM227 B

AJNMkswR…SnXAFUHL AbbB8JjN…Dn5A3JhA

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.

7.243 × 10⁹³(94-digit number)

72439196712142259688…32589325624576537439

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

7.243 × 10⁹³(94-digit number)

72439196712142259688…32589325624576537439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.243 × 10⁹³(94-digit number)

72439196712142259688…32589325624576537441

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

1.448 × 10⁹⁴(95-digit number)

14487839342428451937…65178651249153074879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.448 × 10⁹⁴(95-digit number)

14487839342428451937…65178651249153074881

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

2.897 × 10⁹⁴(95-digit number)

28975678684856903875…30357302498306149759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.897 × 10⁹⁴(95-digit number)

28975678684856903875…30357302498306149761

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

5.795 × 10⁹⁴(95-digit number)

57951357369713807750…60714604996612299519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.795 × 10⁹⁴(95-digit number)

57951357369713807750…60714604996612299521

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

1.159 × 10⁹⁵(96-digit number)

11590271473942761550…21429209993224599039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.159 × 10⁹⁵(96-digit number)

11590271473942761550…21429209993224599041

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 #192,553

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