Home/Chain Registry/Block #80,083

Block #80,083

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 10:18:04 PM · Difficulty 9.2473 · 6,718,789 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f21c06254bfae4c5a2dc3903688139a930830bac2e29f18e7cda2700172022e3

View on Chainz ↗

Height

#80,083

Difficulty

9.247294

Transactions

Size

206 B

Version

Bits

093f4ea1

Nonce

Timestamp

7/23/2013, 10:18:04 PM

Confirmations

6,718,789

Merkle Root

15fa0c01cd5d68da3d32ae0575e53a72742d6ed264439374e89bac61282106df

Transactions (1)

Coinbase15fa0c01cd5d68…9bac61282106df

1 in → 1 out11.6800 XPM110 B

AJ8tmsUS…nLBcDVkU

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.

1.476 × 10¹⁰⁹(110-digit number)

14764945796970888654…11271027629611224400

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

1.476 × 10¹⁰⁹(110-digit number)

14764945796970888654…11271027629611224399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.476 × 10¹⁰⁹(110-digit number)

14764945796970888654…11271027629611224401

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

2.952 × 10¹⁰⁹(110-digit number)

29529891593941777308…22542055259222448799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.952 × 10¹⁰⁹(110-digit number)

29529891593941777308…22542055259222448801

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

5.905 × 10¹⁰⁹(110-digit number)

59059783187883554616…45084110518444897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.905 × 10¹⁰⁹(110-digit number)

59059783187883554616…45084110518444897601

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

1.181 × 10¹¹⁰(111-digit number)

11811956637576710923…90168221036889795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.181 × 10¹¹⁰(111-digit number)

11811956637576710923…90168221036889795201

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

2.362 × 10¹¹⁰(111-digit number)

23623913275153421846…80336442073779590399

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 80083

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 f21c06254bfae4c5a2dc3903688139a930830bac2e29f18e7cda2700172022e3

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 #80,083 on Chainz ↗