Home/Chain Registry/Block #99,903

Block #99,903

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/5/2013, 9:59:32 PM · Difficulty 9.4061 · 6,701,953 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82de338e781a0f82efa1402d715428dbaddf014822c65e31cc1282d7bca140b4

View on Chainz ↗

Height

#99,903

Difficulty

9.406115

Transactions

Size

205 B

Version

Bits

0967f726

Nonce

42,394

Timestamp

8/5/2013, 9:59:32 PM

Confirmations

6,701,953

Merkle Root

7ad2467e7f403ff767a5c3da80b2e716c2412fa90a77e67cda9651f81308ee6e

Transactions (1)

Coinbase7ad2467e7f403f…9651f81308ee6e

1 in → 1 out11.2900 XPM109 B

AHpT5Ubr…ErRZ8yTA

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.

1.041 × 10¹¹⁰(111-digit number)

10419810738970838725…72327489307418310240

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

1.041 × 10¹¹⁰(111-digit number)

10419810738970838725…72327489307418310239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.041 × 10¹¹⁰(111-digit number)

10419810738970838725…72327489307418310241

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

2.083 × 10¹¹⁰(111-digit number)

20839621477941677451…44654978614836620479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.083 × 10¹¹⁰(111-digit number)

20839621477941677451…44654978614836620481

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

4.167 × 10¹¹⁰(111-digit number)

41679242955883354903…89309957229673240959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.167 × 10¹¹⁰(111-digit number)

41679242955883354903…89309957229673240961

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

8.335 × 10¹¹⁰(111-digit number)

83358485911766709807…78619914459346481919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.335 × 10¹¹⁰(111-digit number)

83358485911766709807…78619914459346481921

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

1.667 × 10¹¹¹(112-digit number)

16671697182353341961…57239828918692963839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.667 × 10¹¹¹(112-digit number)

16671697182353341961…57239828918692963841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 99903

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 82de338e781a0f82efa1402d715428dbaddf014822c65e31cc1282d7bca140b4

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 #99,903 on Chainz ↗