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Block #264,605

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/18/2013, 8:31:58 PM Β· Difficulty 9.9640 Β· 6,533,909 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0fa30c032086d4eb488e14c0f3d6e70e9f4a6b97a4355e99c38f5065adafa7e3
View on Chainz β†—

Height

#264,605

Difficulty

9.964029

Transactions

1

Size

206 B

Version

2

Bits

09f6ca95

Nonce

143,518

Timestamp

11/18/2013, 8:31:58 PM

Confirmations

6,533,909

Merkle Root

e4e32295c69287cf2729752469dde5d0c76d4e29805ba74d98cd3f8974c1e754
Transactions (1)
Coinbasee4e32295c69287…cd3f8974c1e754
1 in β†’ 1 out10.0600 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.

2.003 Γ— 10⁹⁡(96-digit number)
20032895052991039377…00351380611618570240
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
2.003 Γ— 10⁹⁡(96-digit number)
20032895052991039377…00351380611618570239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.006 Γ— 10⁹⁡(96-digit number)
40065790105982078754…00702761223237140479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.013 Γ— 10⁹⁡(96-digit number)
80131580211964157508…01405522446474280959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.602 Γ— 10⁹⁢(97-digit number)
16026316042392831501…02811044892948561919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.205 Γ— 10⁹⁢(97-digit number)
32052632084785663003…05622089785897123839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.410 Γ— 10⁹⁢(97-digit number)
64105264169571326006…11244179571794247679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.282 Γ— 10⁹⁷(98-digit number)
12821052833914265201…22488359143588495359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.564 Γ— 10⁹⁷(98-digit number)
25642105667828530402…44976718287176990719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.128 Γ— 10⁹⁷(98-digit number)
51284211335657060805…89953436574353981439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.025 Γ— 10⁹⁸(99-digit number)
10256842267131412161…79906873148707962879
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 264605

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 0fa30c032086d4eb488e14c0f3d6e70e9f4a6b97a4355e99c38f5065adafa7e3

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 #264,605 on Chainz β†—
Circulating Supply:57,632,125 XPMΒ·at block #6,798,513 Β· updates every 60s
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