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Block #30,302

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 6:35:06 PM Β· Difficulty 7.9866 Β· 6,779,971 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3956bca3944f26e23ddf92d0e0ed4f1b184049a06c3e46bc329d830ae831a448
View on Chainz β†—

Height

#30,302

Difficulty

7.986589

Transactions

2

Size

353 B

Version

2

Bits

07fc9120

Nonce

156

Timestamp

7/13/2013, 6:35:06 PM

Confirmations

6,779,971

Merkle Root

28419630d44fa2de9a498aa09757880d4c880dc690b2ec835159edb9cb0bc302
Transactions (2)
Coinbasec20856c1207462…4a95867568951c
1 in β†’ 1 out15.6700 XPM108 B
AKSwr9eU…dLNxuVyn
14dc25fed3bb60…81088fe170d99a
1 in β†’ 1 out15.8500 XPM157 B
ALHZoZL6…jmQF6een
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.

2.158 Γ— 10⁹⁰(91-digit number)
21586383450684510843…16089203288901584600
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
2.158 Γ— 10⁹⁰(91-digit number)
21586383450684510843…16089203288901584599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.317 Γ— 10⁹⁰(91-digit number)
43172766901369021686…32178406577803169199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.634 Γ— 10⁹⁰(91-digit number)
86345533802738043373…64356813155606338399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.726 Γ— 10⁹¹(92-digit number)
17269106760547608674…28713626311212676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.453 Γ— 10⁹¹(92-digit number)
34538213521095217349…57427252622425353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.907 Γ— 10⁹¹(92-digit number)
69076427042190434698…14854505244850707199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.381 Γ— 10⁹²(93-digit number)
13815285408438086939…29709010489701414399
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 30302

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 3956bca3944f26e23ddf92d0e0ed4f1b184049a06c3e46bc329d830ae831a448

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 #30,302 on Chainz β†—
Circulating Supply:57,726,257 XPMΒ·at block #6,810,272 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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