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Block #241,485

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/3/2013, 5:59:18 AM Β· Difficulty 9.9580 Β· 6,591,452 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3f2d98b89add0287f849d3fafe48ed74aa67677846028ce9b62d42d4b53e2240
View on Chainz β†—

Height

#241,485

Difficulty

9.957955

Transactions

1

Size

234 B

Version

2

Bits

09f53c8f

Nonce

21,150

Timestamp

11/3/2013, 5:59:18 AM

Confirmations

6,591,452

Merkle Root

b817ddbcc371a271b7b5cb2c783022f54b1c6bbe79ca04a4382efb813103b0ee
Transactions (1)
Coinbaseb817ddbcc371a2…2efb813103b0ee
1 in β†’ 2 out10.0700 XPM142 B
AKcbk49N…GJbKa7j1AHsw4d6U…EnM8UXNZ
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.

6.717 Γ— 10⁹⁸(99-digit number)
67170366428684001273…48607862278279166080
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
6.717 Γ— 10⁹⁸(99-digit number)
67170366428684001273…48607862278279166079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁹(100-digit number)
13434073285736800254…97215724556558332159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.686 Γ— 10⁹⁹(100-digit number)
26868146571473600509…94431449113116664319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.373 Γ— 10⁹⁹(100-digit number)
53736293142947201018…88862898226233328639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.074 Γ— 10¹⁰⁰(101-digit number)
10747258628589440203…77725796452466657279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.149 Γ— 10¹⁰⁰(101-digit number)
21494517257178880407…55451592904933314559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.298 Γ— 10¹⁰⁰(101-digit number)
42989034514357760814…10903185809866629119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.597 Γ— 10¹⁰⁰(101-digit number)
85978069028715521629…21806371619733258239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.719 Γ— 10¹⁰¹(102-digit number)
17195613805743104325…43612743239466516479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.439 Γ— 10¹⁰¹(102-digit number)
34391227611486208651…87225486478933032959
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 241485

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 3f2d98b89add0287f849d3fafe48ed74aa67677846028ce9b62d42d4b53e2240

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 #241,485 on Chainz β†—
Circulating Supply:57,907,673 XPMΒ·at block #6,832,936 Β· updates every 60s
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