Home/Chain Registry/Block #76,413

Block #76,413

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 12:25:56 AM · Difficulty 9.0960 · 6,714,793 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9568d2ae15cdac99263d01db35e0e9a4b5d00c6cbb51b00a581068e709e8011c

View on Chainz ↗

Height

#76,413

Difficulty

9.095990

Transactions

Size

207 B

Version

Bits

091892c7

Nonce

149

Timestamp

7/22/2013, 12:25:56 AM

Confirmations

6,714,793

Merkle Root

0a827d159ab017f0dbdd52aff9e067264fea3b5b9762a1d7c71e78b6ab833825

Transactions (1)

Coinbase0a827d159ab017…1e78b6ab833825

1 in → 1 out12.0700 XPM110 B

ANey87HK…MGUx5bYr

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.

2.341 × 10¹¹¹(112-digit number)

23410635437544619440…72894890485129220050

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

2.341 × 10¹¹¹(112-digit number)

23410635437544619440…72894890485129220049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.341 × 10¹¹¹(112-digit number)

23410635437544619440…72894890485129220051

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

4.682 × 10¹¹¹(112-digit number)

46821270875089238880…45789780970258440099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.682 × 10¹¹¹(112-digit number)

46821270875089238880…45789780970258440101

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

9.364 × 10¹¹¹(112-digit number)

93642541750178477760…91579561940516880199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.364 × 10¹¹¹(112-digit number)

93642541750178477760…91579561940516880201

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

1.872 × 10¹¹²(113-digit number)

18728508350035695552…83159123881033760399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.872 × 10¹¹²(113-digit number)

18728508350035695552…83159123881033760401

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

3.745 × 10¹¹²(113-digit number)

37457016700071391104…66318247762067520799

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 76413

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 9568d2ae15cdac99263d01db35e0e9a4b5d00c6cbb51b00a581068e709e8011c

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 #76,413 on Chainz ↗