Home/Chain Registry/Block #78,216

Block #78,216

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 5:48:52 PM · Difficulty 9.2232 · 6,714,845 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8cce5ad3f519ab40616c48e3bf2f7d121aa1c9d80cf666825cb7e7edaa7bff3f

View on Chainz ↗

Height

#78,216

Difficulty

9.223161

Transactions

Size

208 B

Version

Bits

0939210e

Nonce

416

Timestamp

7/22/2013, 5:48:52 PM

Confirmations

6,714,845

Merkle Root

82a66df01e2ceb7fac0a0964fbbd07e3f05806b33b7c8535109c0b942e8141a3

Transactions (1)

Coinbase82a66df01e2ceb…9c0b942e8141a3

1 in → 1 out11.7400 XPM110 B

AaAGK47z…gLkb6ziB

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.

4.642 × 10¹¹²(113-digit number)

46423356703221264447…78334087398036131330

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

4.642 × 10¹¹²(113-digit number)

46423356703221264447…78334087398036131329

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.642 × 10¹¹²(113-digit number)

46423356703221264447…78334087398036131331

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

9.284 × 10¹¹²(113-digit number)

92846713406442528894…56668174796072262659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.284 × 10¹¹²(113-digit number)

92846713406442528894…56668174796072262661

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

1.856 × 10¹¹³(114-digit number)

18569342681288505778…13336349592144525319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.856 × 10¹¹³(114-digit number)

18569342681288505778…13336349592144525321

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

3.713 × 10¹¹³(114-digit number)

37138685362577011557…26672699184289050639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.713 × 10¹¹³(114-digit number)

37138685362577011557…26672699184289050641

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

7.427 × 10¹¹³(114-digit number)

74277370725154023115…53345398368578101279

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 78216

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 8cce5ad3f519ab40616c48e3bf2f7d121aa1c9d80cf666825cb7e7edaa7bff3f

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 #78,216 on Chainz ↗