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Block #418,586

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/25/2014, 12:19:35 AM Β· Difficulty 10.3854 Β· 6,395,286 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
69cc9f6600a14448d5579d5cb1d1645e04f763b3c76915ae1c53d70648313227
View on Chainz β†—

Height

#418,586

Difficulty

10.385426

Transactions

1

Size

202 B

Version

2

Bits

0a62ab4e

Nonce

622,919

Timestamp

2/25/2014, 12:19:35 AM

Confirmations

6,395,286

Merkle Root

7f7b8c0eb46206c68725928712fe95eaf35a86dadb6fbc078d78f5cc803f0555
Transactions (1)
Coinbase7f7b8c0eb46206…78f5cc803f0555
1 in β†’ 1 out9.2600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.475 Γ— 10⁹⁸(99-digit number)
24755880519275811297…33257103962589739680
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
2.475 Γ— 10⁹⁸(99-digit number)
24755880519275811297…33257103962589739679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.951 Γ— 10⁹⁸(99-digit number)
49511761038551622595…66514207925179479359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.902 Γ— 10⁹⁸(99-digit number)
99023522077103245191…33028415850358958719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.980 Γ— 10⁹⁹(100-digit number)
19804704415420649038…66056831700717917439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.960 Γ— 10⁹⁹(100-digit number)
39609408830841298076…32113663401435834879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.921 Γ— 10⁹⁹(100-digit number)
79218817661682596153…64227326802871669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.584 Γ— 10¹⁰⁰(101-digit number)
15843763532336519230…28454653605743339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.168 Γ— 10¹⁰⁰(101-digit number)
31687527064673038461…56909307211486679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.337 Γ— 10¹⁰⁰(101-digit number)
63375054129346076922…13818614422973358079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.267 Γ— 10¹⁰¹(102-digit number)
12675010825869215384…27637228845946716159
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 418586

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 69cc9f6600a14448d5579d5cb1d1645e04f763b3c76915ae1c53d70648313227

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 #418,586 on Chainz β†—
Circulating Supply:57,755,050 XPMΒ·at block #6,813,871 Β· updates every 60s
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