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Block #291,427

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/3/2013, 4:34:11 AM Β· Difficulty 9.9898 Β· 6,535,560 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d158c069bf469bb8153556f65e8925111ad2641e1a4002a05da72ff3bcfedc9
View on Chainz β†—

Height

#291,427

Difficulty

9.989841

Transactions

1

Size

200 B

Version

2

Bits

09fd663b

Nonce

179,711

Timestamp

12/3/2013, 4:34:11 AM

Confirmations

6,535,560

Merkle Root

19858ac7623fa5666bd0709392bc520c645b30d8f83483f3c887bff76b8f881a
Transactions (1)
Coinbase19858ac7623fa5…87bff76b8f881a
1 in β†’ 1 out10.0100 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.

4.343 Γ— 10⁹⁴(95-digit number)
43437297396949505950…12927015579932891840
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
4.343 Γ— 10⁹⁴(95-digit number)
43437297396949505950…12927015579932891839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.687 Γ— 10⁹⁴(95-digit number)
86874594793899011901…25854031159865783679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.737 Γ— 10⁹⁡(96-digit number)
17374918958779802380…51708062319731567359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.474 Γ— 10⁹⁡(96-digit number)
34749837917559604760…03416124639463134719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.949 Γ— 10⁹⁡(96-digit number)
69499675835119209521…06832249278926269439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.389 Γ— 10⁹⁢(97-digit number)
13899935167023841904…13664498557852538879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.779 Γ— 10⁹⁢(97-digit number)
27799870334047683808…27328997115705077759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.559 Γ— 10⁹⁢(97-digit number)
55599740668095367617…54657994231410155519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.111 Γ— 10⁹⁷(98-digit number)
11119948133619073523…09315988462820311039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.223 Γ— 10⁹⁷(98-digit number)
22239896267238147046…18631976925640622079
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 291427

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 4d158c069bf469bb8153556f65e8925111ad2641e1a4002a05da72ff3bcfedc9

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 #291,427 on Chainz β†—
Circulating Supply:57,860,071 XPMΒ·at block #6,826,986 Β· updates every 60s
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