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Block #241,235

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/3/2013, 2:24:07 AM Β· Difficulty 9.9577 Β· 6,575,999 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4c55abcc21c625fa42f6efbfcf2a43ea02e7971f0b290fc8c728acdbb39f16e4
View on Chainz β†—

Height

#241,235

Difficulty

9.957662

Transactions

1

Size

198 B

Version

2

Bits

09f5295b

Nonce

180,568

Timestamp

11/3/2013, 2:24:07 AM

Confirmations

6,575,999

Merkle Root

a0428fa2f738a16b327e2447b0d0ff72aa92ef24012a69651ce27fcd21c3edb3
Transactions (1)
Coinbasea0428fa2f738a1…e27fcd21c3edb3
1 in β†’ 1 out10.0700 XPM109 B
Ae64wR7h…XBJ5uXf3
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.

1.017 Γ— 10⁹³(94-digit number)
10171637034489178950…95328878662269841280
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
1.017 Γ— 10⁹³(94-digit number)
10171637034489178950…95328878662269841279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.034 Γ— 10⁹³(94-digit number)
20343274068978357901…90657757324539682559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.068 Γ— 10⁹³(94-digit number)
40686548137956715802…81315514649079365119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.137 Γ— 10⁹³(94-digit number)
81373096275913431604…62631029298158730239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.627 Γ— 10⁹⁴(95-digit number)
16274619255182686320…25262058596317460479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.254 Γ— 10⁹⁴(95-digit number)
32549238510365372641…50524117192634920959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.509 Γ— 10⁹⁴(95-digit number)
65098477020730745283…01048234385269841919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.301 Γ— 10⁹⁡(96-digit number)
13019695404146149056…02096468770539683839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.603 Γ— 10⁹⁡(96-digit number)
26039390808292298113…04192937541079367679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.207 Γ— 10⁹⁡(96-digit number)
52078781616584596226…08385875082158735359
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 241235

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 4c55abcc21c625fa42f6efbfcf2a43ea02e7971f0b290fc8c728acdbb39f16e4

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 #241,235 on Chainz β†—
Circulating Supply:57,781,911 XPMΒ·at block #6,817,233 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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