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Block #418,891

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/25/2014, 5:39:22 AM Β· Difficulty 10.3846 Β· 6,407,323 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d06a6f05e43e0f824558edf43715df7dadfae3761f6e866310aab224d9a81efd
View on Chainz β†—

Height

#418,891

Difficulty

10.384551

Transactions

1

Size

203 B

Version

2

Bits

0a6271ec

Nonce

1,164

Timestamp

2/25/2014, 5:39:22 AM

Confirmations

6,407,323

Merkle Root

2d371fd640b9313fad7a04a27e184667056d6b88b0cf6f8f025613b8abecf072
Transactions (1)
Coinbase2d371fd640b931…5613b8abecf072
1 in β†’ 1 out9.2600 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.

6.211 Γ— 10¹⁰²(103-digit number)
62116869761240742169…66108792084308843520
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
6.211 Γ— 10¹⁰²(103-digit number)
62116869761240742169…66108792084308843519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.242 Γ— 10¹⁰³(104-digit number)
12423373952248148433…32217584168617687039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.484 Γ— 10¹⁰³(104-digit number)
24846747904496296867…64435168337235374079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.969 Γ— 10¹⁰³(104-digit number)
49693495808992593735…28870336674470748159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.938 Γ— 10¹⁰³(104-digit number)
99386991617985187471…57740673348941496319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.987 Γ— 10¹⁰⁴(105-digit number)
19877398323597037494…15481346697882992639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.975 Γ— 10¹⁰⁴(105-digit number)
39754796647194074988…30962693395765985279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.950 Γ— 10¹⁰⁴(105-digit number)
79509593294388149977…61925386791531970559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.590 Γ— 10¹⁰⁡(106-digit number)
15901918658877629995…23850773583063941119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.180 Γ— 10¹⁰⁡(106-digit number)
31803837317755259990…47701547166127882239
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 418891

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 d06a6f05e43e0f824558edf43715df7dadfae3761f6e866310aab224d9a81efd

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 #418,891 on Chainz β†—
Circulating Supply:57,853,844 XPMΒ·at block #6,826,213 Β· updates every 60s
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