Home/Chain Registry/Block #76,354

Block #76,354

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 11:43:01 PM · Difficulty 9.0920 · 6,727,577 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

18beb4618bfaf01dbbfce5fe7e7f6412bfd5ea963df0ae444e431fb99974ce4a

View on Chainz ↗

Height

#76,354

Difficulty

9.091985

Transactions

Size

203 B

Version

Bits

09178c56

Nonce

585

Timestamp

7/21/2013, 11:43:01 PM

Confirmations

6,727,577

Merkle Root

cd1b82c97f08d03f897739412f46003b2f72a928c67ac6eb3c86032d351928bf

Transactions (1)

Coinbasecd1b82c97f08d0…86032d351928bf

1 in → 1 out12.0800 XPM110 B

AYGjxbdf…YFHt1cSm

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.

5.619 × 10¹⁰¹(102-digit number)

56193663508744234798…85239659654604654220

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

5.619 × 10¹⁰¹(102-digit number)

56193663508744234798…85239659654604654219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.619 × 10¹⁰¹(102-digit number)

56193663508744234798…85239659654604654221

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

1.123 × 10¹⁰²(103-digit number)

11238732701748846959…70479319309209308439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.123 × 10¹⁰²(103-digit number)

11238732701748846959…70479319309209308441

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

2.247 × 10¹⁰²(103-digit number)

22477465403497693919…40958638618418616879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.247 × 10¹⁰²(103-digit number)

22477465403497693919…40958638618418616881

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

4.495 × 10¹⁰²(103-digit number)

44954930806995387838…81917277236837233759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.495 × 10¹⁰²(103-digit number)

44954930806995387838…81917277236837233761

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

8.990 × 10¹⁰²(103-digit number)

89909861613990775677…63834554473674467519

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 76354

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 18beb4618bfaf01dbbfce5fe7e7f6412bfd5ea963df0ae444e431fb99974ce4a

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 #76,354 on Chainz ↗