Block #1,387,341

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2015, 12:10:54 PM · Difficulty 10.8134 · 5,426,519 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

953b794ecdd4f911c99d429b712964e2ce5bbeaec31dbbd698bf1abbd4e900ae

View on Chainz ↗

Height

#1,387,341

Difficulty

10.813409

Transactions

Size

1.15 KB

Version

Bits

0ad03b98

Nonce

527,226,190

Timestamp

12/27/2015, 12:10:54 PM

Confirmations

5,426,519

Mined by

⛏️ P2SHAUVP8jD3wcdGke9Cr8AWDhuG8otmYJMLiZ

Merkle Root

58894b7703c57629b11fc780bbc615bbd252081e54cb69ed7520fc512030362a

Transactions (2)

Coinbaseec07d976a76ca4…51cc6d46e9e37d

1 in → 1 out8.5500 XPM109 B

AUVP8jD3…tmYJMLiZ

c2f1854958a7a8…859f76bc58312e

1 in → 24 out121.6160 XPM974 B

AKaz3dni…sbqBja51 AXn94E9d…xKzG1Yrs AUZVgZfv…emr2TwrC APGdziGW…3ou8jPJi AVEYJtbR…Zqkssptv

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.

1.865 × 10⁹⁶(97-digit number)

18652547873213180158…37307809328326202879

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

1.865 × 10⁹⁶(97-digit number)

18652547873213180158…37307809328326202879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.865 × 10⁹⁶(97-digit number)

18652547873213180158…37307809328326202881

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

3.730 × 10⁹⁶(97-digit number)

37305095746426360316…74615618656652405759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.730 × 10⁹⁶(97-digit number)

37305095746426360316…74615618656652405761

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

7.461 × 10⁹⁶(97-digit number)

74610191492852720632…49231237313304811519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.461 × 10⁹⁶(97-digit number)

74610191492852720632…49231237313304811521

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

1.492 × 10⁹⁷(98-digit number)

14922038298570544126…98462474626609623039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.492 × 10⁹⁷(98-digit number)

14922038298570544126…98462474626609623041

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

2.984 × 10⁹⁷(98-digit number)

29844076597141088252…96924949253219246079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.984 × 10⁹⁷(98-digit number)

29844076597141088252…96924949253219246081

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 #1,387,341

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