Block #27,351

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 8:33:59 AM · Difficulty 7.9785 · 6,783,742 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0164c94c74988e0eaa1f64d2c0f56c909d28df8cc47161594f5684f437f359a0

View on Chainz ↗

Height

#27,351

Difficulty

7.978511

Transactions

Size

574 B

Version

Bits

07fa7fb0

Nonce

233

Timestamp

7/13/2013, 8:33:59 AM

Confirmations

6,783,742

Mined by

⛏️ P2SHAKY7vyUa5ExpEdK18nN1JjxoambJcqmnwE

Merkle Root

818ce995d9c1cebe9bd196e8f07c6bc8dd1c92ed911d2d468709ca5c56c4b373

Transactions (2)

Coinbase0b90be047ad5f8…5f18d9cc1c9d9c

1 in → 1 out15.7000 XPM109 B

AKY7vyUa…bJcqmnwE

e4243be4598ad0…d0e0205f36695a

2 in → 2 out189.1100 XPM375 B

APPE6HXG…kFh2gAw4 AU4AxAzL…y8DH19oQ

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.

7.206 × 10⁹⁴(95-digit number)

72065184507344827169…72702913034365333479

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

7.206 × 10⁹⁴(95-digit number)

72065184507344827169…72702913034365333479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.206 × 10⁹⁴(95-digit number)

72065184507344827169…72702913034365333481

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

1.441 × 10⁹⁵(96-digit number)

14413036901468965433…45405826068730666959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.441 × 10⁹⁵(96-digit number)

14413036901468965433…45405826068730666961

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

2.882 × 10⁹⁵(96-digit number)

28826073802937930867…90811652137461333919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.882 × 10⁹⁵(96-digit number)

28826073802937930867…90811652137461333921

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

5.765 × 10⁹⁵(96-digit number)

57652147605875861735…81623304274922667839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.765 × 10⁹⁵(96-digit number)

57652147605875861735…81623304274922667841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #27,351

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