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Block #367,141

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/19/2014, 9:02:32 PM Β· Difficulty 10.4357 Β· 6,447,081 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
85b38f5167d2c8c8b1798bc2fc3e9fda09fbf980111d47de87af6dd4a95ed957
View on Chainz β†—

Height

#367,141

Difficulty

10.435701

Transactions

1

Size

201 B

Version

2

Bits

0a6f8a1e

Nonce

179,772

Timestamp

1/19/2014, 9:02:32 PM

Confirmations

6,447,081

Merkle Root

76e659ecf29ec35e3341ed80431dd2e63c31e40de901066e3a423f01c7d9d238
Transactions (1)
Coinbase76e659ecf29ec3…423f01c7d9d238
1 in β†’ 1 out9.1700 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.

3.241 Γ— 10⁹⁷(98-digit number)
32417606736671171227…60610448472977396640
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
3.241 Γ— 10⁹⁷(98-digit number)
32417606736671171227…60610448472977396639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.483 Γ— 10⁹⁷(98-digit number)
64835213473342342455…21220896945954793279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.296 Γ— 10⁹⁸(99-digit number)
12967042694668468491…42441793891909586559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.593 Γ— 10⁹⁸(99-digit number)
25934085389336936982…84883587783819173119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.186 Γ— 10⁹⁸(99-digit number)
51868170778673873964…69767175567638346239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.037 Γ— 10⁹⁹(100-digit number)
10373634155734774792…39534351135276692479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.074 Γ— 10⁹⁹(100-digit number)
20747268311469549585…79068702270553384959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.149 Γ— 10⁹⁹(100-digit number)
41494536622939099171…58137404541106769919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.298 Γ— 10⁹⁹(100-digit number)
82989073245878198343…16274809082213539839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.659 Γ— 10¹⁰⁰(101-digit number)
16597814649175639668…32549618164427079679
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 367141

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 85b38f5167d2c8c8b1798bc2fc3e9fda09fbf980111d47de87af6dd4a95ed957

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 #367,141 on Chainz β†—
Circulating Supply:57,757,845 XPMΒ·at block #6,814,221 Β· updates every 60s
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