Home/Chain Registry/Block #81,546

Block #81,546

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 8:18:02 PM · Difficulty 9.2684 · 6,709,516 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a9b396a1ef356d073902e4f16a05a8af83d25eaa3faa0a1dd93a95231b5e0df

View on Chainz ↗

Height

#81,546

Difficulty

9.268366

Transactions

Size

209 B

Version

Bits

0944b3a4

Nonce

202,306

Timestamp

7/24/2013, 8:18:02 PM

Confirmations

6,709,516

Merkle Root

c9ee6d74f6b74cf31f7edb80de0280536bbe0dd53ba7068c7fe45e019c15c14a

Transactions (1)

Coinbasec9ee6d74f6b74c…e45e019c15c14a

1 in → 1 out11.6200 XPM109 B

AeExP7Rg…4kvHCTvA

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.

1.878 × 10¹¹⁹(120-digit number)

18781742300339719075…79096122819869507730

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

1.878 × 10¹¹⁹(120-digit number)

18781742300339719075…79096122819869507729

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.878 × 10¹¹⁹(120-digit number)

18781742300339719075…79096122819869507731

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

3.756 × 10¹¹⁹(120-digit number)

37563484600679438150…58192245639739015459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.756 × 10¹¹⁹(120-digit number)

37563484600679438150…58192245639739015461

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

7.512 × 10¹¹⁹(120-digit number)

75126969201358876301…16384491279478030919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.512 × 10¹¹⁹(120-digit number)

75126969201358876301…16384491279478030921

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

1.502 × 10¹²⁰(121-digit number)

15025393840271775260…32768982558956061839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.502 × 10¹²⁰(121-digit number)

15025393840271775260…32768982558956061841

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

3.005 × 10¹²⁰(121-digit number)

30050787680543550520…65537965117912123679

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 81546

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 3a9b396a1ef356d073902e4f16a05a8af83d25eaa3faa0a1dd93a95231b5e0df

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 #81,546 on Chainz ↗