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Block #41,689

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 5:06:17 PM · Difficulty 8.5452 · 6,750,642 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

93a3ce05a1947fe253092bf3e7e3bfa7985005f42f688d3d800ffe14ee4d5a06

View on Chainz ↗

Height

#41,689

Difficulty

8.545216

Transactions

Size

206 B

Version

Bits

088b934a

Nonce

297

Timestamp

7/14/2013, 5:06:17 PM

Confirmations

6,750,642

Merkle Root

33dd6a0d6ce21f2171e2ef0fe637af9a50f4721df1aefeb74ec0a08c2148976e

Transactions (1)

Coinbase33dd6a0d6ce21f…c0a08c2148976e

1 in → 1 out13.6800 XPM109 B

AambLBsx…GaJ1ipEX

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.

1.878 × 10¹¹⁰(111-digit number)

18789348701662137087…95695978016698047050

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

1.878 × 10¹¹⁰(111-digit number)

18789348701662137087…95695978016698047049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.878 × 10¹¹⁰(111-digit number)

18789348701662137087…95695978016698047051

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

3.757 × 10¹¹⁰(111-digit number)

37578697403324274175…91391956033396094099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.757 × 10¹¹⁰(111-digit number)

37578697403324274175…91391956033396094101

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

7.515 × 10¹¹⁰(111-digit number)

75157394806648548350…82783912066792188199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.515 × 10¹¹⁰(111-digit number)

75157394806648548350…82783912066792188201

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

1.503 × 10¹¹¹(112-digit number)

15031478961329709670…65567824133584376399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.503 × 10¹¹¹(112-digit number)

15031478961329709670…65567824133584376401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 8

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 41689

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 93a3ce05a1947fe253092bf3e7e3bfa7985005f42f688d3d800ffe14ee4d5a06

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #41,689 on Chainz ↗