Block #180,727

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/26/2013, 12:52:01 AM · Difficulty 9.8617 · 6,622,729 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

976cfc45752e3e1f1152493a2f13f6f881e794a7c589e91f7ac324ee69c65bf2

View on Chainz ↗

Height

#180,727

Difficulty

9.861716

Transactions

Size

2.26 KB

Version

Bits

09dc9967

Nonce

9,121

Timestamp

9/26/2013, 12:52:01 AM

Confirmations

6,622,729

Mined by

⛏️ P2SHAVZgkCcWPrF4B5ENWiQHiKUwrnyETyJHFA

Merkle Root

8bcddbd0a52957f6002d2da3ad616e53641bdbf984d786b432289ad6e7814ba5

Transactions (3)

Coinbased98e5c74669fc5…a552cc36eb73ce

1 in → 1 out10.3000 XPM109 B

AVZgkCcW…yETyJHFA

9824c406d475e7…29a525a1f2b522

10 in → 2 out94.1700 XPM1.23 KB

AKaGKSaU…SdAqshJU AZiZ3BSK…ouABkYiL

8a0eb65e662618…fccc843a165bbb

6 in → 2 out37.1460 XPM864 B

AbJEGmBt…MUK7h8UH ARyYtqtL…uCP66s1P

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.

5.709 × 10⁹²(93-digit number)

57092476434587515999…56323516201909299199

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

5.709 × 10⁹²(93-digit number)

57092476434587515999…56323516201909299199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.709 × 10⁹²(93-digit number)

57092476434587515999…56323516201909299201

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

1.141 × 10⁹³(94-digit number)

11418495286917503199…12647032403818598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.141 × 10⁹³(94-digit number)

11418495286917503199…12647032403818598401

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

2.283 × 10⁹³(94-digit number)

22836990573835006399…25294064807637196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.283 × 10⁹³(94-digit number)

22836990573835006399…25294064807637196801

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

4.567 × 10⁹³(94-digit number)

45673981147670012799…50588129615274393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.567 × 10⁹³(94-digit number)

45673981147670012799…50588129615274393601

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

9.134 × 10⁹³(94-digit number)

91347962295340025599…01176259230548787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.134 × 10⁹³(94-digit number)

91347962295340025599…01176259230548787201

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