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Block #588,102

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/14/2014, 9:10:33 AM Β· Difficulty 10.9501 Β· 6,238,797 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9e14c38756f1cb58418778f6515abf601ed1f2201a24c7c6056d72d30ebdc42d
View on Chainz β†—

Height

#588,102

Difficulty

10.950099

Transactions

1

Size

207 B

Version

2

Bits

0af339b7

Nonce

2,219,729,284

Timestamp

6/14/2014, 9:10:33 AM

Confirmations

6,238,797

Merkle Root

cfe058924003316dec223f524d04ed7f786e7dbe14175275385acd9e1aba463d
Transactions (1)
Coinbasecfe05892400331…5acd9e1aba463d
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.894 Γ— 10⁹⁷(98-digit number)
18945310421935182228…61559699540065372800
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
1.894 Γ— 10⁹⁷(98-digit number)
18945310421935182228…61559699540065372801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.789 Γ— 10⁹⁷(98-digit number)
37890620843870364456…23119399080130745601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.578 Γ— 10⁹⁷(98-digit number)
75781241687740728912…46238798160261491201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.515 Γ— 10⁹⁸(99-digit number)
15156248337548145782…92477596320522982401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.031 Γ— 10⁹⁸(99-digit number)
30312496675096291564…84955192641045964801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.062 Γ— 10⁹⁸(99-digit number)
60624993350192583129…69910385282091929601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.212 Γ— 10⁹⁹(100-digit number)
12124998670038516625…39820770564183859201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.424 Γ— 10⁹⁹(100-digit number)
24249997340077033251…79641541128367718401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.849 Γ— 10⁹⁹(100-digit number)
48499994680154066503…59283082256735436801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.699 Γ— 10⁹⁹(100-digit number)
96999989360308133007…18566164513470873601
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 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
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 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 588102

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 9e14c38756f1cb58418778f6515abf601ed1f2201a24c7c6056d72d30ebdc42d

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 #588,102 on Chainz β†—
Circulating Supply:57,859,358 XPMΒ·at block #6,826,898 Β· updates every 60s
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