Home/Chain Registry/Block #83,468

Block #83,468

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 4:24:24 AM · Difficulty 9.2679 · 6,706,503 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44d509efe24e828e3575cf956cff4c855404bf48a5cadcfc3680c52b9657e298

View on Chainz ↗

Height

#83,468

Difficulty

9.267883

Transactions

Size

203 B

Version

Bits

094493fd

Nonce

170,077

Timestamp

7/26/2013, 4:24:24 AM

Confirmations

6,706,503

Merkle Root

124400232b5a8fae5c16d4cedc80c108bef770d45594ee888b11bf7d2de95c07

Transactions (1)

Coinbase124400232b5a8f…11bf7d2de95c07

1 in → 1 out11.6300 XPM109 B

AcuJraLT…Y66BS47Q

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.

7.102 × 10¹⁰³(104-digit number)

71022499932188139900…55752936668914812400

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

7.102 × 10¹⁰³(104-digit number)

71022499932188139900…55752936668914812399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.102 × 10¹⁰³(104-digit number)

71022499932188139900…55752936668914812401

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

1.420 × 10¹⁰⁴(105-digit number)

14204499986437627980…11505873337829624799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.420 × 10¹⁰⁴(105-digit number)

14204499986437627980…11505873337829624801

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

2.840 × 10¹⁰⁴(105-digit number)

28408999972875255960…23011746675659249599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.840 × 10¹⁰⁴(105-digit number)

28408999972875255960…23011746675659249601

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

5.681 × 10¹⁰⁴(105-digit number)

56817999945750511920…46023493351318499199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.681 × 10¹⁰⁴(105-digit number)

56817999945750511920…46023493351318499201

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

1.136 × 10¹⁰⁵(106-digit number)

11363599989150102384…92046986702636998399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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 83468

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 44d509efe24e828e3575cf956cff4c855404bf48a5cadcfc3680c52b9657e298

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 #83,468 on Chainz ↗