XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #497,728

Block #497,728

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/17/2014, 5:43:39 PM Β· Difficulty 10.7719 Β· 6,303,529 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8cf9a2102aa896a2d6866742d89982048c8ebf04296e7d36f87ccc48e39df5bb
View on Chainz β†—

Height

#497,728

Difficulty

10.771860

Transactions

1

Size

207 B

Version

2

Bits

0ac598a1

Nonce

73,752,419

Timestamp

4/17/2014, 5:43:39 PM

Confirmations

6,303,529

Merkle Root

5175ca3e948e632fba3124f65537cb6f8c415c81573e904ed1cef0787539d46c
Transactions (1)
Coinbase5175ca3e948e63…cef0787539d46c
1 in β†’ 1 out8.6000 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) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.912 Γ— 10⁹⁷(98-digit number)
29123471216603886790…12863941344955860500
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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.

1
origin βˆ’ 1
2.912 Γ— 10⁹⁷(98-digit number)
29123471216603886790…12863941344955860499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.824 Γ— 10⁹⁷(98-digit number)
58246942433207773581…25727882689911720999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁸(99-digit number)
11649388486641554716…51455765379823441999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.329 Γ— 10⁹⁸(99-digit number)
23298776973283109432…02911530759646883999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.659 Γ— 10⁹⁸(99-digit number)
46597553946566218865…05823061519293767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.319 Γ— 10⁹⁸(99-digit number)
93195107893132437730…11646123038587535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.863 Γ— 10⁹⁹(100-digit number)
18639021578626487546…23292246077175071999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.727 Γ— 10⁹⁹(100-digit number)
37278043157252975092…46584492154350143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.455 Γ— 10⁹⁹(100-digit number)
74556086314505950184…93168984308700287999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.491 Γ— 10¹⁰⁰(101-digit number)
14911217262901190036…86337968617400575999
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 497728

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 8cf9a2102aa896a2d6866742d89982048c8ebf04296e7d36f87ccc48e39df5bb

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 β†’ Debug Window β†’ 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 #497,728 on Chainz β†—
Circulating Supply:57,654,125 XPMΒ·at block #6,801,256 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK