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Block #225,418

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/24/2013, 11:35:00 AM Β· Difficulty 9.9367 Β· 6,570,536 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f8df020fe0afa3d64374d8b2c9999896f4e2c1fe8d8de59750fef6d73b5fe03a
View on Chainz β†—

Height

#225,418

Difficulty

9.936673

Transactions

1

Size

206 B

Version

2

Bits

09efc9d4

Nonce

120,366

Timestamp

10/24/2013, 11:35:00 AM

Confirmations

6,570,536

Merkle Root

51b6a013ce9c05ee1f34ddd1e7448481fb9d923db61b6db31c832b5a8e7cb075
Transactions (1)
Coinbase51b6a013ce9c05…832b5a8e7cb075
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

6.512 Γ— 10⁹³(94-digit number)
65127263551798461148…29962388752563128320
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
6.512 Γ— 10⁹³(94-digit number)
65127263551798461148…29962388752563128321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.302 Γ— 10⁹⁴(95-digit number)
13025452710359692229…59924777505126256641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.605 Γ— 10⁹⁴(95-digit number)
26050905420719384459…19849555010252513281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.210 Γ— 10⁹⁴(95-digit number)
52101810841438768918…39699110020505026561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.042 Γ— 10⁹⁡(96-digit number)
10420362168287753783…79398220041010053121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.084 Γ— 10⁹⁡(96-digit number)
20840724336575507567…58796440082020106241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.168 Γ— 10⁹⁡(96-digit number)
41681448673151015134…17592880164040212481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.336 Γ— 10⁹⁡(96-digit number)
83362897346302030269…35185760328080424961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.667 Γ— 10⁹⁢(97-digit number)
16672579469260406053…70371520656160849921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.334 Γ— 10⁹⁢(97-digit number)
33345158938520812107…40743041312321699841
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 225418

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 f8df020fe0afa3d64374d8b2c9999896f4e2c1fe8d8de59750fef6d73b5fe03a

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 #225,418 on Chainz β†—
Circulating Supply:57,611,722 XPMΒ·at block #6,795,953 Β· updates every 60s
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