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Block #241,188

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/3/2013, 1:32:48 AM Β· Difficulty 9.9577 Β· 6,589,699 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
db96db0503f1b96dcf1697aa90f4006dfa6b6a4f87ddc732e64e0d389bbcb966
View on Chainz β†—

Height

#241,188

Difficulty

9.957691

Transactions

1

Size

204 B

Version

2

Bits

09f52b38

Nonce

33,887

Timestamp

11/3/2013, 1:32:48 AM

Confirmations

6,589,699

Merkle Root

53a398bfa4086b1b4813db9a9effbf204938617792fa04263a6ed6b667b856bf
Transactions (1)
Coinbase53a398bfa4086b…6ed6b667b856bf
1 in β†’ 1 out10.0700 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.

2.077 Γ— 10⁸⁹(90-digit number)
20778319150443279292…90751920836360519250
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
2.077 Γ— 10⁸⁹(90-digit number)
20778319150443279292…90751920836360519249
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.155 Γ— 10⁸⁹(90-digit number)
41556638300886558584…81503841672721038499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.311 Γ— 10⁸⁹(90-digit number)
83113276601773117168…63007683345442076999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.662 Γ— 10⁹⁰(91-digit number)
16622655320354623433…26015366690884153999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.324 Γ— 10⁹⁰(91-digit number)
33245310640709246867…52030733381768307999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.649 Γ— 10⁹⁰(91-digit number)
66490621281418493734…04061466763536615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.329 Γ— 10⁹¹(92-digit number)
13298124256283698746…08122933527073231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.659 Γ— 10⁹¹(92-digit number)
26596248512567397493…16245867054146463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.319 Γ— 10⁹¹(92-digit number)
53192497025134794987…32491734108292927999
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 241188

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 db96db0503f1b96dcf1697aa90f4006dfa6b6a4f87ddc732e64e0d389bbcb966

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 #241,188 on Chainz β†—
Circulating Supply:57,891,233 XPMΒ·at block #6,830,886 Β· updates every 60s
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