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Block #294,832

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2013, 2:35:14 AM Β· Difficulty 9.9912 Β· 6,512,037 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f2c945a9d82ceed736478dfe2bc87d4b5c9e7fc2b4df302b41c07c2a6cbffc69
View on Chainz β†—

Height

#294,832

Difficulty

9.991161

Transactions

1

Size

207 B

Version

2

Bits

09fdbcbe

Nonce

2,754

Timestamp

12/5/2013, 2:35:14 AM

Confirmations

6,512,037

Merkle Root

50070d6006e2ce0046a600edcde7de4fa569109c6c41e3bd89c9c16ae71d0064
Transactions (1)
Coinbase50070d6006e2ce…c9c16ae71d0064
1 in β†’ 1 out10.0000 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.

6.273 Γ— 10⁹⁷(98-digit number)
62738356897319089068…23122097681543418240
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
6.273 Γ— 10⁹⁷(98-digit number)
62738356897319089068…23122097681543418239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.254 Γ— 10⁹⁸(99-digit number)
12547671379463817813…46244195363086836479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.509 Γ— 10⁹⁸(99-digit number)
25095342758927635627…92488390726173672959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.019 Γ— 10⁹⁸(99-digit number)
50190685517855271254…84976781452347345919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.003 Γ— 10⁹⁹(100-digit number)
10038137103571054250…69953562904694691839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.007 Γ— 10⁹⁹(100-digit number)
20076274207142108501…39907125809389383679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.015 Γ— 10⁹⁹(100-digit number)
40152548414284217003…79814251618778767359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.030 Γ— 10⁹⁹(100-digit number)
80305096828568434007…59628503237557534719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.606 Γ— 10¹⁰⁰(101-digit number)
16061019365713686801…19257006475115069439
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 294832

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 f2c945a9d82ceed736478dfe2bc87d4b5c9e7fc2b4df302b41c07c2a6cbffc69

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 #294,832 on Chainz β†—
Circulating Supply:57,699,059 XPMΒ·at block #6,806,868 Β· updates every 60s
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