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Block #267,053

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/20/2013, 10:35:32 PM Β· Difficulty 9.9599 Β· 6,558,493 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b03e025ca05114271876bd41cad00f1446ba44aebc2978b0d272fc5a2c3d9fc5
View on Chainz β†—

Height

#267,053

Difficulty

9.959936

Transactions

1

Size

199 B

Version

2

Bits

09f5be5f

Nonce

816,580

Timestamp

11/20/2013, 10:35:32 PM

Confirmations

6,558,493

Merkle Root

b07c3e0286d21dfe4994d7195a5d65d999e2fc1372d73cb6256cce1ac9faa2e6
Transactions (1)
Coinbaseb07c3e0286d21d…6cce1ac9faa2e6
1 in β†’ 1 out10.0700 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.

2.876 Γ— 10⁹³(94-digit number)
28766328760846115499…09849625673910750320
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
2.876 Γ— 10⁹³(94-digit number)
28766328760846115499…09849625673910750319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.753 Γ— 10⁹³(94-digit number)
57532657521692230998…19699251347821500639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.150 Γ— 10⁹⁴(95-digit number)
11506531504338446199…39398502695643001279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.301 Γ— 10⁹⁴(95-digit number)
23013063008676892399…78797005391286002559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.602 Γ— 10⁹⁴(95-digit number)
46026126017353784798…57594010782572005119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.205 Γ— 10⁹⁴(95-digit number)
92052252034707569597…15188021565144010239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.841 Γ— 10⁹⁡(96-digit number)
18410450406941513919…30376043130288020479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.682 Γ— 10⁹⁡(96-digit number)
36820900813883027838…60752086260576040959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.364 Γ— 10⁹⁡(96-digit number)
73641801627766055677…21504172521152081919
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 267053

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 b03e025ca05114271876bd41cad00f1446ba44aebc2978b0d272fc5a2c3d9fc5

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 #267,053 on Chainz β†—
Circulating Supply:57,848,468 XPMΒ·at block #6,825,545 Β· updates every 60s
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