Block #1,491,451

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2016, 5:06:36 PM · Difficulty 10.6835 · 5,322,783 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e06f4f97905d0b8d85b91742a8ed213e02cded4ad8e4336282c52875f46c6f77

View on Chainz ↗

Height

#1,491,451

Difficulty

10.683460

Transactions

Size

3.10 KB

Version

Bits

0aaef73f

Nonce

1,484,604,487

Timestamp

3/10/2016, 5:06:36 PM

Confirmations

5,322,783

Mined by

⛏️ P2SHAdqXHx2PgLfXUZ46e4ByFZ4rgW53wTYfEq

Merkle Root

d1e139d49af92a798b91a6bd6af2eed6cc567d5dfd431b18de1be39630fa76c1

Transactions (2)

Coinbase2f534c126ba00a…ebfe18407c059d

1 in → 1 out8.7800 XPM109 B

AdqXHx2P…53wTYfEq

8eb9942a41b31a…ab6fb6716962a9

1 in → 83 out202.2995 XPM2.91 KB

AawB1NhV…oYZTQfdb AXtshJoo…bJuHUssu AToLzNHA…8kcfz3bv AS31eLZn…ASReVtDE APGdziGW…3ou8jPJi

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.

4.421 × 10⁹⁷(98-digit number)

44219083497538726305…95233804455901009919

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

4.421 × 10⁹⁷(98-digit number)

44219083497538726305…95233804455901009919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.421 × 10⁹⁷(98-digit number)

44219083497538726305…95233804455901009921

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

8.843 × 10⁹⁷(98-digit number)

88438166995077452610…90467608911802019839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.843 × 10⁹⁷(98-digit number)

88438166995077452610…90467608911802019841

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

1.768 × 10⁹⁸(99-digit number)

17687633399015490522…80935217823604039679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.768 × 10⁹⁸(99-digit number)

17687633399015490522…80935217823604039681

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

3.537 × 10⁹⁸(99-digit number)

35375266798030981044…61870435647208079359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.537 × 10⁹⁸(99-digit number)

35375266798030981044…61870435647208079361

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

7.075 × 10⁹⁸(99-digit number)

70750533596061962088…23740871294416158719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.075 × 10⁹⁸(99-digit number)

70750533596061962088…23740871294416158721

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 #1,491,451

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