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Block #514

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/8/2013, 1:23:04 AM Β· Difficulty 7.0206 Β· 6,796,083 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c05bafa31892cbdfc52818737aeedf87605ef3085a2be97f4bb52461b4eaef06
View on Chainz β†—

Height

#514

Difficulty

7.020634

Transactions

1

Size

195 B

Version

2

Bits

0705483f

Nonce

272

Timestamp

7/8/2013, 1:23:04 AM

Confirmations

6,796,083

Merkle Root

018feac58bbe125ba2d45e7dadda08ffe69ed329697077f10f2166a1e5b80393
Transactions (1)
Coinbase018feac58bbe12…2166a1e5b80393
1 in β†’ 1 out20.2600 XPM108 B
AMqUNXEt…YKyzL6uS
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.

2.895 Γ— 10⁸⁸(89-digit number)
28950537510822539783…06821303128851496250
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
2.895 Γ— 10⁸⁸(89-digit number)
28950537510822539783…06821303128851496251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.790 Γ— 10⁸⁸(89-digit number)
57901075021645079567…13642606257702992501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.158 Γ— 10⁸⁹(90-digit number)
11580215004329015913…27285212515405985001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.316 Γ— 10⁸⁹(90-digit number)
23160430008658031826…54570425030811970001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.632 Γ— 10⁸⁹(90-digit number)
46320860017316063653…09140850061623940001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.264 Γ— 10⁸⁹(90-digit number)
92641720034632127307…18281700123247880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.852 Γ— 10⁹⁰(91-digit number)
18528344006926425461…36563400246495760001
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 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 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 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 514

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 c05bafa31892cbdfc52818737aeedf87605ef3085a2be97f4bb52461b4eaef06

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 #514 on Chainz β†—
Circulating Supply:57,616,779 XPMΒ·at block #6,796,596 Β· updates every 60s
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