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Home/Chain Registry/Block #244,731

Block #244,731

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/5/2013, 1:31:19 AM Β· Difficulty 9.9631 Β· 6,556,814 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5ea24993a01024cc57f9be4dcf56105da64a6b411c4bc8900c19cfaa7ac43772
View on Chainz β†—

Height

#244,731

Difficulty

9.963093

Transactions

1

Size

206 B

Version

2

Bits

09f68d46

Nonce

76,364

Timestamp

11/5/2013, 1:31:19 AM

Confirmations

6,556,814

Merkle Root

8caadefb517719ad68f26239925f0001b40d76d55733d5cbe532920067754bdf
Transactions (1)
Coinbase8caadefb517719…32920067754bdf
1 in β†’ 1 out10.0600 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.

3.975 Γ— 10⁹⁴(95-digit number)
39758202854413614251…05201986132641061120
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
3.975 Γ— 10⁹⁴(95-digit number)
39758202854413614251…05201986132641061119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.951 Γ— 10⁹⁴(95-digit number)
79516405708827228503…10403972265282122239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.590 Γ— 10⁹⁡(96-digit number)
15903281141765445700…20807944530564244479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.180 Γ— 10⁹⁡(96-digit number)
31806562283530891401…41615889061128488959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.361 Γ— 10⁹⁡(96-digit number)
63613124567061782802…83231778122256977919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.272 Γ— 10⁹⁢(97-digit number)
12722624913412356560…66463556244513955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.544 Γ— 10⁹⁢(97-digit number)
25445249826824713121…32927112489027911679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.089 Γ— 10⁹⁢(97-digit number)
50890499653649426242…65854224978055823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.017 Γ— 10⁹⁷(98-digit number)
10178099930729885248…31708449956111646719
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 244731

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 5ea24993a01024cc57f9be4dcf56105da64a6b411c4bc8900c19cfaa7ac43772

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 #244,731 on Chainz β†—
Circulating Supply:57,656,440 XPMΒ·at block #6,801,544 Β· updates every 60s
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