Block #1,462,429

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2016, 5:04:15 AM · Difficulty 10.7837 · 5,362,861 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab42bc35ad8c52c50cec483272689a3b37fbeca818a5e71d10cd71ce781675ad

View on Chainz ↗

Height

#1,462,429

Difficulty

10.783696

Transactions

Size

868 B

Version

Bits

0ac8a054

Nonce

1,265,323,153

Timestamp

2/18/2016, 5:04:15 AM

Confirmations

5,362,861

Mined by

⛏️ P2SHAWkcgAmhbfCW4BmykRRyHcpctH19RzzqFe

Merkle Root

3660819065e1b76ebae3d6c017df329a79d3dafa5e760422df8a4a91e202a7d8

Transactions (2)

Coinbasea0b51c103582bb…914b911fe16405

1 in → 1 out8.6000 XPM110 B

AWkcgAmh…19RzzqFe

e17f86c842bcac…e2a5e00fc93991

1 in → 15 out188.7252 XPM667 B

APMuRBbN…ebDYT21o AMpzuq4o…QT51NNUE AcGQTaEA…HP3EaDJ9 AT1oTbdU…zkY2kuSH Aahuyvry…34ytp7AN

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.

2.119 × 10⁹⁶(97-digit number)

21198780433533831885…55781298006905274879

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

2.119 × 10⁹⁶(97-digit number)

21198780433533831885…55781298006905274879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.119 × 10⁹⁶(97-digit number)

21198780433533831885…55781298006905274881

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

4.239 × 10⁹⁶(97-digit number)

42397560867067663770…11562596013810549759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.239 × 10⁹⁶(97-digit number)

42397560867067663770…11562596013810549761

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

8.479 × 10⁹⁶(97-digit number)

84795121734135327540…23125192027621099519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.479 × 10⁹⁶(97-digit number)

84795121734135327540…23125192027621099521

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

1.695 × 10⁹⁷(98-digit number)

16959024346827065508…46250384055242199039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.695 × 10⁹⁷(98-digit number)

16959024346827065508…46250384055242199041

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

3.391 × 10⁹⁷(98-digit number)

33918048693654131016…92500768110484398079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.391 × 10⁹⁷(98-digit number)

33918048693654131016…92500768110484398081

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 #1,462,429

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