Block #1,453,083

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/12/2016, 11:47:47 AM · Difficulty 10.7301 · 5,364,154 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3eec460cbeef4e9831de359719a8d524371ad3c06a6f781300a8366fc40bee33

View on Chainz ↗

Height

#1,453,083

Difficulty

10.730149

Transactions

Size

1.28 KB

Version

Bits

0abaeb05

Nonce

764,119,110

Timestamp

2/12/2016, 11:47:47 AM

Confirmations

5,364,154

Mined by

⛏️ P2SHANKAPe2eHV57xaND3cCGXDBUrZPZVD6kox

Merkle Root

af99c60e367c1ce67af88240fe14d15cbbd7f31dc576b77dd8aebfcc316997c4

Transactions (2)

Coinbaseb5558a1fa7ada7…e1321402e1b1bf

1 in → 1 out8.6900 XPM109 B

ANKAPe2e…PZVD6kox

d8e1c4f2298bc9…9966ba20551e81

7 in → 2 out60.0429 XPM1.09 KB

AQcjeddP…AoqhXrhG ALi9D4mQ…dXPqkrjS

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.

1.763 × 10⁹⁸(99-digit number)

17634062124562143994…13644873140426342399

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

1.763 × 10⁹⁸(99-digit number)

17634062124562143994…13644873140426342399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.763 × 10⁹⁸(99-digit number)

17634062124562143994…13644873140426342401

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

3.526 × 10⁹⁸(99-digit number)

35268124249124287989…27289746280852684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.526 × 10⁹⁸(99-digit number)

35268124249124287989…27289746280852684801

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

7.053 × 10⁹⁸(99-digit number)

70536248498248575979…54579492561705369599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.053 × 10⁹⁸(99-digit number)

70536248498248575979…54579492561705369601

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

1.410 × 10⁹⁹(100-digit number)

14107249699649715195…09158985123410739199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.410 × 10⁹⁹(100-digit number)

14107249699649715195…09158985123410739201

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

2.821 × 10⁹⁹(100-digit number)

28214499399299430391…18317970246821478399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.821 × 10⁹⁹(100-digit number)

28214499399299430391…18317970246821478401

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 #1,453,083

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