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Block #63,318

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 12:42:34 AM Β· Difficulty 8.9789 Β· 6,761,926 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2bd54f0b257fd8eeb69e7797ffef6e34b0b74b0bfa1d74a2740c2260ee107e35
View on Chainz β†—

Height

#63,318

Difficulty

8.978858

Transactions

1

Size

199 B

Version

2

Bits

08fa966b

Nonce

130

Timestamp

7/19/2013, 12:42:34 AM

Confirmations

6,761,926

Merkle Root

457e29e9075c6f66484b6059a62d8e530d2671ad63d33dd90921510264014755
Transactions (1)
Coinbase457e29e9075c6f…21510264014755
1 in β†’ 1 out12.3900 XPM110 B
AH3bk8oh…33SrZ2yc
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.

1.063 Γ— 10⁹³(94-digit number)
10636614769935060361…00487949434795818490
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.063 Γ— 10⁹³(94-digit number)
10636614769935060361…00487949434795818491
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.127 Γ— 10⁹³(94-digit number)
21273229539870120723…00975898869591636981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.254 Γ— 10⁹³(94-digit number)
42546459079740241447…01951797739183273961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.509 Γ— 10⁹³(94-digit number)
85092918159480482894…03903595478366547921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.701 Γ— 10⁹⁴(95-digit number)
17018583631896096578…07807190956733095841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.403 Γ— 10⁹⁴(95-digit number)
34037167263792193157…15614381913466191681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.807 Γ— 10⁹⁴(95-digit number)
68074334527584386315…31228763826932383361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.361 Γ— 10⁹⁡(96-digit number)
13614866905516877263…62457527653864766721
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second 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 8
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 63318

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 2bd54f0b257fd8eeb69e7797ffef6e34b0b74b0bfa1d74a2740c2260ee107e35

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 #63,318 on Chainz β†—
Circulating Supply:57,846,046 XPMΒ·at block #6,825,243 Β· updates every 60s
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