Block #15,225

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 6:55:04 PM · Difficulty 7.8467 · 6,780,198 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d749593e15fc6642509cd0d7419c8e7efd998055c21d785af49e56b44a38a398

View on Chainz ↗

Height

#15,225

Difficulty

7.846651

Transactions

Size

667 B

Version

Bits

07d8be27

Nonce

436

Timestamp

7/11/2013, 6:55:04 PM

Confirmations

6,780,198

Mined by

⛏️ P2SHAG4TgV8uGaHTQzmYhY6bUb1zSsQvpXGs8i

Merkle Root

24bc316ca4a082ec29c8454b2f35e34f05ec661be8cb74a15a6e4a27d83f37ae

Transactions (3)

Coinbaseb8d4e58cc31340…59f1ddec3cb4a1

1 in → 1 out16.2400 XPM108 B

AG4TgV8u…QvpXGs8i

f8914a093a79e9…73df551cbcc0ef

1 in → 1 out16.9200 XPM158 B

AU4AxAzL…y8DH19oQ

2eb8680191b71c…1cef7eafab08a2

2 in → 1 out50.5900 XPM307 B

Ad3hHLDx…mq8Afkvv

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.

6.431 × 10¹⁰⁴(105-digit number)

64318277371036610227…06235635001730439359

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

6.431 × 10¹⁰⁴(105-digit number)

64318277371036610227…06235635001730439359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.431 × 10¹⁰⁴(105-digit number)

64318277371036610227…06235635001730439361

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

1.286 × 10¹⁰⁵(106-digit number)

12863655474207322045…12471270003460878719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.286 × 10¹⁰⁵(106-digit number)

12863655474207322045…12471270003460878721

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

2.572 × 10¹⁰⁵(106-digit number)

25727310948414644091…24942540006921757439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.572 × 10¹⁰⁵(106-digit number)

25727310948414644091…24942540006921757441

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

5.145 × 10¹⁰⁵(106-digit number)

51454621896829288182…49885080013843514879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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