Home/Chain Registry/Block #87,694

Block #87,694

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 2:27:02 AM · Difficulty 9.2716 · 6,703,404 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e11dd23ad81164bb2fd92204ac2997fb7bc2fe7ff51c2e0e80c8ba004701dfd

View on Chainz ↗

Height

#87,694

Difficulty

9.271591

Transactions

Size

205 B

Version

Bits

09458705

Nonce

246,623

Timestamp

7/29/2013, 2:27:02 AM

Confirmations

6,703,404

Merkle Root

9ddd7385f120ec42390c54d6f9b0d52f7ae31c019ea9deca287d604449fc2111

Transactions (1)

Coinbase9ddd7385f120ec…7d604449fc2111

1 in → 1 out11.6200 XPM109 B

AcBadmkp…GmhL921o

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.

1.880 × 10¹⁰⁸(109-digit number)

18805338257978602722…73655518941978469240

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

1.880 × 10¹⁰⁸(109-digit number)

18805338257978602722…73655518941978469239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.880 × 10¹⁰⁸(109-digit number)

18805338257978602722…73655518941978469241

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

3.761 × 10¹⁰⁸(109-digit number)

37610676515957205445…47311037883956938479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.761 × 10¹⁰⁸(109-digit number)

37610676515957205445…47311037883956938481

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

7.522 × 10¹⁰⁸(109-digit number)

75221353031914410891…94622075767913876959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.522 × 10¹⁰⁸(109-digit number)

75221353031914410891…94622075767913876961

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

1.504 × 10¹⁰⁹(110-digit number)

15044270606382882178…89244151535827753919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.504 × 10¹⁰⁹(110-digit number)

15044270606382882178…89244151535827753921

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

3.008 × 10¹⁰⁹(110-digit number)

30088541212765764356…78488303071655507839

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 87694

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 2e11dd23ad81164bb2fd92204ac2997fb7bc2fe7ff51c2e0e80c8ba004701dfd

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 #87,694 on Chainz ↗