Home/Chain Registry/Block #111,085

Block #111,085

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/11/2013, 6:54:42 AM · Difficulty 9.7024 · 6,715,873 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

303b94f6e7dfdb2a1b38a85ee5ad3940a45af729e2599e80bf24e56cd9df9c7d

View on Chainz ↗

Height

#111,085

Difficulty

9.702359

Transactions

Size

202 B

Version

Bits

09b3cdce

Nonce

49,029

Timestamp

8/11/2013, 6:54:42 AM

Confirmations

6,715,873

Merkle Root

59decce1d5bc667988af5364cbbc97821d3f92f815654987c0df6f72ebfaab19

Transactions (1)

Coinbase59decce1d5bc66…df6f72ebfaab19

1 in → 1 out10.6100 XPM109 B

AGNF5FM1…n54CJy51

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.

1.382 × 10¹⁰¹(102-digit number)

13829735563964892881…86000725241743985230

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

1.382 × 10¹⁰¹(102-digit number)

13829735563964892881…86000725241743985229

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.382 × 10¹⁰¹(102-digit number)

13829735563964892881…86000725241743985231

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

2.765 × 10¹⁰¹(102-digit number)

27659471127929785762…72001450483487970459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.765 × 10¹⁰¹(102-digit number)

27659471127929785762…72001450483487970461

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

5.531 × 10¹⁰¹(102-digit number)

55318942255859571525…44002900966975940919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.531 × 10¹⁰¹(102-digit number)

55318942255859571525…44002900966975940921

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

1.106 × 10¹⁰²(103-digit number)

11063788451171914305…88005801933951881839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.106 × 10¹⁰²(103-digit number)

11063788451171914305…88005801933951881841

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

2.212 × 10¹⁰²(103-digit number)

22127576902343828610…76011603867903763679

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 111085

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 303b94f6e7dfdb2a1b38a85ee5ad3940a45af729e2599e80bf24e56cd9df9c7d

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 #111,085 on Chainz ↗

Block #111,085

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