Home/Chain Registry/Block #91,380

Block #91,380

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/31/2013, 9:42:15 PM · Difficulty 9.2194 · 6,698,671 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2585e12c9afeb16c901b6532d94c9d09e8608ff46f4d920848a7647b7a75cea9

View on Chainz ↗

Height

#91,380

Difficulty

9.219406

Transactions

Size

207 B

Version

Bits

09382b00

Nonce

200,209

Timestamp

7/31/2013, 9:42:15 PM

Confirmations

6,698,671

Merkle Root

f9037f2d80c92bb93aefea850c3b13ebbef05add2940798fc6913391238ff1bb

Transactions (1)

Coinbasef9037f2d80c92b…913391238ff1bb

1 in → 1 out11.7500 XPM112 B

AT5A2KL6…CT16n6i2

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.

1.007 × 10¹⁰⁷(108-digit number)

10072206293846570980…47635319138794459200

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

1.007 × 10¹⁰⁷(108-digit number)

10072206293846570980…47635319138794459199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.007 × 10¹⁰⁷(108-digit number)

10072206293846570980…47635319138794459201

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

2.014 × 10¹⁰⁷(108-digit number)

20144412587693141960…95270638277588918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.014 × 10¹⁰⁷(108-digit number)

20144412587693141960…95270638277588918401

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

4.028 × 10¹⁰⁷(108-digit number)

40288825175386283920…90541276555177836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.028 × 10¹⁰⁷(108-digit number)

40288825175386283920…90541276555177836801

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

8.057 × 10¹⁰⁷(108-digit number)

80577650350772567841…81082553110355673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.057 × 10¹⁰⁷(108-digit number)

80577650350772567841…81082553110355673601

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

1.611 × 10¹⁰⁸(109-digit number)

16115530070154513568…62165106220711347199

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 91380

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 2585e12c9afeb16c901b6532d94c9d09e8608ff46f4d920848a7647b7a75cea9

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 #91,380 on Chainz ↗