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Block #294,179

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/4/2013, 5:50:14 PM Β· Difficulty 9.9909 Β· 6,530,627 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dfe532f6004e4499aaeb5751bbaf39ee198d25605c102a2a936a3e33a9ee7c13
View on Chainz β†—

Height

#294,179

Difficulty

9.990918

Transactions

1

Size

207 B

Version

2

Bits

09fdacd4

Nonce

7,258

Timestamp

12/4/2013, 5:50:14 PM

Confirmations

6,530,627

Merkle Root

3fd5bd5f5b053e17058e691443b6bf48a82ac6fbabcd080f5ed2844f7685ab0b
Transactions (1)
Coinbase3fd5bd5f5b053e…d2844f7685ab0b
1 in β†’ 1 out10.0000 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.

2.025 Γ— 10⁹⁸(99-digit number)
20251912846327785473…91758174386808929920
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
2.025 Γ— 10⁹⁸(99-digit number)
20251912846327785473…91758174386808929919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.050 Γ— 10⁹⁸(99-digit number)
40503825692655570946…83516348773617859839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.100 Γ— 10⁹⁸(99-digit number)
81007651385311141892…67032697547235719679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.620 Γ— 10⁹⁹(100-digit number)
16201530277062228378…34065395094471439359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.240 Γ— 10⁹⁹(100-digit number)
32403060554124456757…68130790188942878719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.480 Γ— 10⁹⁹(100-digit number)
64806121108248913514…36261580377885757439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.296 Γ— 10¹⁰⁰(101-digit number)
12961224221649782702…72523160755771514879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.592 Γ— 10¹⁰⁰(101-digit number)
25922448443299565405…45046321511543029759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.184 Γ— 10¹⁰⁰(101-digit number)
51844896886599130811…90092643023086059519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.036 Γ— 10¹⁰¹(102-digit number)
10368979377319826162…80185286046172119039
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 294179

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 dfe532f6004e4499aaeb5751bbaf39ee198d25605c102a2a936a3e33a9ee7c13

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 #294,179 on Chainz β†—
Circulating Supply:57,842,524 XPMΒ·at block #6,824,805 Β· updates every 60s
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