Home/Chain Registry/Block #498,501

Block #498,501

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/18/2014, 3:26:07 AM · Difficulty 10.7804 · 6,291,576 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

fb9f5b60ec7d79625dc70fc982d3ccc7bcbcde9a7c9edfa153eef9ffb212e8ab

View on Chainz ↗

Height

#498,501

Difficulty

10.780394

Transactions

Size

207 B

Version

Bits

0ac7c7e2

Nonce

119,840,645

Timestamp

4/18/2014, 3:26:07 AM

Confirmations

6,291,576

Merkle Root

71bc2b6719d14cc231abdd137dc7ad3f4a96a6ad16b9db0bb01fe011830f9746

Transactions (1)

Coinbase71bc2b6719d14c…1fe011830f9746

1 in → 1 out8.5900 XPM116 B

AbwWkWZt…kawDhufa

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.

6.261 × 10⁹⁷(98-digit number)

62617568388215753507…78660576721534204880

Discovered Prime Numbers

p_k = 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.

origin − 1

6.261 × 10⁹⁷(98-digit number)

62617568388215753507…78660576721534204879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.252 × 10⁹⁸(99-digit number)

12523513677643150701…57321153443068409759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.504 × 10⁹⁸(99-digit number)

25047027355286301403…14642306886136819519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.009 × 10⁹⁸(99-digit number)

50094054710572602806…29284613772273639039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.001 × 10⁹⁹(100-digit number)

10018810942114520561…58569227544547278079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.003 × 10⁹⁹(100-digit number)

20037621884229041122…17138455089094556159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.007 × 10⁹⁹(100-digit number)

40075243768458082245…34276910178189112319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.015 × 10⁹⁹(100-digit number)

80150487536916164490…68553820356378224639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.603 × 10¹⁰⁰(101-digit number)

16030097507383232898…37107640712756449279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.206 × 10¹⁰⁰(101-digit number)

32060195014766465796…74215281425512898559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 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 498501

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 fb9f5b60ec7d79625dc70fc982d3ccc7bcbcde9a7c9edfa153eef9ffb212e8ab

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 #498,501 on Chainz ↗