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Block #498,572

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/18/2014, 4:24:49 AM Β· Difficulty 10.7809 Β· 6,328,058 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ef5a7a86fe7bdd894d3df7a3a8cbf4799e8c3258adc544d019253ad8756d0cc7
View on Chainz β†—

Height

#498,572

Difficulty

10.780924

Transactions

1

Size

203 B

Version

2

Bits

0ac7eaa2

Nonce

259,585,426

Timestamp

4/18/2014, 4:24:49 AM

Confirmations

6,328,058

Merkle Root

13b339d72e24f3e329193f53e12c7a9c5cdd9779050d92b3e3e080a346f72b0f
Transactions (1)
Coinbase13b339d72e24f3…e080a346f72b0f
1 in β†’ 1 out8.5900 XPM111 B
AXq9joE1…tdvz7Few
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.

1.242 Γ— 10⁹⁹(100-digit number)
12428475435138321538…94837551078665996800
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
1.242 Γ— 10⁹⁹(100-digit number)
12428475435138321538…94837551078665996801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.485 Γ— 10⁹⁹(100-digit number)
24856950870276643076…89675102157331993601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.971 Γ— 10⁹⁹(100-digit number)
49713901740553286153…79350204314663987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.942 Γ— 10⁹⁹(100-digit number)
99427803481106572307…58700408629327974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.988 Γ— 10¹⁰⁰(101-digit number)
19885560696221314461…17400817258655948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.977 Γ— 10¹⁰⁰(101-digit number)
39771121392442628923…34801634517311897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.954 Γ— 10¹⁰⁰(101-digit number)
79542242784885257846…69603269034623795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.590 Γ— 10¹⁰¹(102-digit number)
15908448556977051569…39206538069247590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.181 Γ— 10¹⁰¹(102-digit number)
31816897113954103138…78413076138495180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.363 Γ— 10¹⁰¹(102-digit number)
63633794227908206276…56826152276990361601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 498572

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 ef5a7a86fe7bdd894d3df7a3a8cbf4799e8c3258adc544d019253ad8756d0cc7

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 #498,572 on Chainz β†—
Circulating Supply:57,857,185 XPMΒ·at block #6,826,629 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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