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Block #264,197

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/18/2013, 11:31:38 AM Β· Difficulty 9.9649 Β· 6,552,528 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4028383d9ee74ee3f1c2c093dd1acf531f9a3ee18c7eda9d28bb3132d35c8f77
View on Chainz β†—

Height

#264,197

Difficulty

9.964939

Transactions

1

Size

198 B

Version

2

Bits

09f70639

Nonce

28,531

Timestamp

11/18/2013, 11:31:38 AM

Confirmations

6,552,528

Merkle Root

f4b157b1c8d02c1f8451305cbcffdf3e97064322d17c14a3c87d16659732311c
Transactions (1)
Coinbasef4b157b1c8d02c…7d16659732311c
1 in β†’ 1 out10.0600 XPM109 B
ASG5oAew…F17gLw13
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.

1.759 Γ— 10⁹¹(92-digit number)
17593874921433686322…26756671204478835840
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
1.759 Γ— 10⁹¹(92-digit number)
17593874921433686322…26756671204478835839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.518 Γ— 10⁹¹(92-digit number)
35187749842867372645…53513342408957671679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.037 Γ— 10⁹¹(92-digit number)
70375499685734745291…07026684817915343359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.407 Γ— 10⁹²(93-digit number)
14075099937146949058…14053369635830686719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.815 Γ— 10⁹²(93-digit number)
28150199874293898116…28106739271661373439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.630 Γ— 10⁹²(93-digit number)
56300399748587796233…56213478543322746879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.126 Γ— 10⁹³(94-digit number)
11260079949717559246…12426957086645493759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.252 Γ— 10⁹³(94-digit number)
22520159899435118493…24853914173290987519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.504 Γ— 10⁹³(94-digit number)
45040319798870236986…49707828346581975039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 264197

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 4028383d9ee74ee3f1c2c093dd1acf531f9a3ee18c7eda9d28bb3132d35c8f77

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 #264,197 on Chainz β†—
Circulating Supply:57,777,834 XPMΒ·at block #6,816,724 Β· updates every 60s
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