Home/Chain Registry/Block #78,381

Block #78,381

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 7:32:16 PM · Difficulty 9.2324 · 6,711,483 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92628a499cd974bc7a0f743b7eda124b7f457690dcf0cb890e9801ec7b3f4355

View on Chainz ↗

Height

#78,381

Difficulty

9.232440

Transactions

Size

874 B

Version

Bits

093b8136

Nonce

347

Timestamp

7/22/2013, 7:32:16 PM

Confirmations

6,711,483

Merkle Root

a5dae60d9ff173e411ff0d8f623bec88d2f36c25108af87dbc022e1fbb917106

Transactions (2)

Coinbaseec34a88a420118…51442514f95d36

1 in → 1 out11.7300 XPM110 B

AYpcPT6a…PXXGqQDn

604a3305a2ac9b…198b4fd6796492

4 in → 2 out749.9112 XPM672 B

AWdzp9VK…cRXYSaSR AcU3G17t…7wPGLC6Z

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.

7.372 × 10⁹⁹(100-digit number)

73728815337264059493…75342954030492849520

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

7.372 × 10⁹⁹(100-digit number)

73728815337264059493…75342954030492849519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.372 × 10⁹⁹(100-digit number)

73728815337264059493…75342954030492849521

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

1.474 × 10¹⁰⁰(101-digit number)

14745763067452811898…50685908060985699039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.474 × 10¹⁰⁰(101-digit number)

14745763067452811898…50685908060985699041

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

2.949 × 10¹⁰⁰(101-digit number)

29491526134905623797…01371816121971398079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.949 × 10¹⁰⁰(101-digit number)

29491526134905623797…01371816121971398081

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

5.898 × 10¹⁰⁰(101-digit number)

58983052269811247594…02743632243942796159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.898 × 10¹⁰⁰(101-digit number)

58983052269811247594…02743632243942796161

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

1.179 × 10¹⁰¹(102-digit number)

11796610453962249518…05487264487885592319

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 78381

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 92628a499cd974bc7a0f743b7eda124b7f457690dcf0cb890e9801ec7b3f4355

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 #78,381 on Chainz ↗