Home/Chain Registry/Block #91,378

Block #91,378

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/31/2013, 9:40:46 PM · Difficulty 9.2194 · 6,698,666 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b4cacd85e80ecdcf3e28a17644fac102b255aef428331f7dded1c1aae492d97

View on Chainz ↗

Height

#91,378

Difficulty

9.219388

Transactions

Size

204 B

Version

Bits

093829d0

Nonce

331,951

Timestamp

7/31/2013, 9:40:46 PM

Confirmations

6,698,666

Merkle Root

edbbcff3e09ef06d268e7e4f052e5a7d9ba214247f7fed07ca8bbc4e54a1d01d

Transactions (1)

Coinbaseedbbcff3e09ef0…8bbc4e54a1d01d

1 in → 1 out11.7500 XPM109 B

AQBxTUro…BbKd3kfh

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.

1.998 × 10¹⁰⁷(108-digit number)

19983895721715427770…14691063669503801280

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

1.998 × 10¹⁰⁷(108-digit number)

19983895721715427770…14691063669503801279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.998 × 10¹⁰⁷(108-digit number)

19983895721715427770…14691063669503801281

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

3.996 × 10¹⁰⁷(108-digit number)

39967791443430855540…29382127339007602559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.996 × 10¹⁰⁷(108-digit number)

39967791443430855540…29382127339007602561

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

7.993 × 10¹⁰⁷(108-digit number)

79935582886861711080…58764254678015205119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.993 × 10¹⁰⁷(108-digit number)

79935582886861711080…58764254678015205121

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

1.598 × 10¹⁰⁸(109-digit number)

15987116577372342216…17528509356030410239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.598 × 10¹⁰⁸(109-digit number)

15987116577372342216…17528509356030410241

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

3.197 × 10¹⁰⁸(109-digit number)

31974233154744684432…35057018712060820479

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 91378

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 2b4cacd85e80ecdcf3e28a17644fac102b255aef428331f7dded1c1aae492d97

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 #91,378 on Chainz ↗