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Block #1,304

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/8/2013, 9:43:32 AM Β· Difficulty 7.0752 Β· 6,825,261 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cf50c94ca51392ce9740b7144f55dcc65ffcdc2209f037ff1adfcf1ca16977bf
View on Chainz β†—

Height

#1,304

Difficulty

7.075180

Transactions

1

Size

203 B

Version

2

Bits

07133f01

Nonce

69

Timestamp

7/8/2013, 9:43:32 AM

Confirmations

6,825,261

Merkle Root

730a129bd8a45b7a1a664dbdf51897ef086e2132e0f190fa748223c216f390f3
Transactions (1)
Coinbase730a129bd8a45b…8223c216f390f3
1 in β†’ 1 out19.9500 XPM108 B
AWJwq2Us…pV9BKzoG
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.

1.254 Γ— 10¹⁰⁢(107-digit number)
12544938194497403646…74820162107979256120
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
1.254 Γ— 10¹⁰⁢(107-digit number)
12544938194497403646…74820162107979256119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.508 Γ— 10¹⁰⁢(107-digit number)
25089876388994807292…49640324215958512239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.017 Γ— 10¹⁰⁢(107-digit number)
50179752777989614584…99280648431917024479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.003 Γ— 10¹⁰⁷(108-digit number)
10035950555597922916…98561296863834048959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.007 Γ— 10¹⁰⁷(108-digit number)
20071901111195845833…97122593727668097919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.014 Γ— 10¹⁰⁷(108-digit number)
40143802222391691667…94245187455336195839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.028 Γ— 10¹⁰⁷(108-digit number)
80287604444783383334…88490374910672391679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 1304

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 cf50c94ca51392ce9740b7144f55dcc65ffcdc2209f037ff1adfcf1ca16977bf

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 #1,304 on Chainz β†—
Circulating Supply:57,856,672 XPMΒ·at block #6,826,564 Β· updates every 60s
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