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Block #265,228

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/19/2013, 9:13:49 AM Β· Difficulty 9.9631 Β· 6,576,186 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de301c5822a4a71cbf1f6c3ee99ec556f80527d968133df87335c7913cfff3ce
View on Chainz β†—

Height

#265,228

Difficulty

9.963070

Transactions

1

Size

202 B

Version

2

Bits

09f68bc3

Nonce

759,427

Timestamp

11/19/2013, 9:13:49 AM

Confirmations

6,576,186

Merkle Root

f063951bee80c60d7f2bc7591b231e298b2e4f6fb0845924fdafaea0c90fef4d
Transactions (1)
Coinbasef063951bee80c6…afaea0c90fef4d
1 in β†’ 1 out10.0600 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.

9.311 Γ— 10⁹⁸(99-digit number)
93118876473369369703…70736060052149667840
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
9.311 Γ— 10⁹⁸(99-digit number)
93118876473369369703…70736060052149667839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.862 Γ— 10⁹⁹(100-digit number)
18623775294673873940…41472120104299335679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.724 Γ— 10⁹⁹(100-digit number)
37247550589347747881…82944240208598671359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.449 Γ— 10⁹⁹(100-digit number)
74495101178695495762…65888480417197342719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.489 Γ— 10¹⁰⁰(101-digit number)
14899020235739099152…31776960834394685439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.979 Γ— 10¹⁰⁰(101-digit number)
29798040471478198304…63553921668789370879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.959 Γ— 10¹⁰⁰(101-digit number)
59596080942956396609…27107843337578741759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.191 Γ— 10¹⁰¹(102-digit number)
11919216188591279321…54215686675157483519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.383 Γ— 10¹⁰¹(102-digit number)
23838432377182558643…08431373350314967039
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 265228

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 de301c5822a4a71cbf1f6c3ee99ec556f80527d968133df87335c7913cfff3ce

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 #265,228 on Chainz β†—
Circulating Supply:57,975,687 XPMΒ·at block #6,841,413 Β· updates every 60s
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