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Block #586,931

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/13/2014, 9:52:39 AM Β· Difficulty 10.9523 Β· 6,227,898 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
68e3b0403d5d6f0acdde92d1fad0f20eca4a92fdca1e300380fbb6ab99c16bdc
View on Chainz β†—

Height

#586,931

Difficulty

10.952269

Transactions

2

Size

582 B

Version

2

Bits

0af3c7ec

Nonce

694,035,084

Timestamp

6/13/2014, 9:52:39 AM

Confirmations

6,227,898

Merkle Root

b91afb4a529771f9be052039398126b067f1559d932f3d45c1d7bf4f93fa5d8a
Transactions (2)
Coinbasee7a84bbf03846d…0296fff810aff5
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
796c7511de7448…eb34cbac264051
2 in β†’ 2 out10.0788 XPM374 B
AUEFYgu3…yCVwYcpyAWAbb2pL…4Wmht5QK
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.

1.305 Γ— 10⁹⁹(100-digit number)
13054301911721003071…53365331051794073600
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
1.305 Γ— 10⁹⁹(100-digit number)
13054301911721003071…53365331051794073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.610 Γ— 10⁹⁹(100-digit number)
26108603823442006142…06730662103588147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.221 Γ— 10⁹⁹(100-digit number)
52217207646884012284…13461324207176294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.044 Γ— 10¹⁰⁰(101-digit number)
10443441529376802456…26922648414352588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.088 Γ— 10¹⁰⁰(101-digit number)
20886883058753604913…53845296828705177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.177 Γ— 10¹⁰⁰(101-digit number)
41773766117507209827…07690593657410355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.354 Γ— 10¹⁰⁰(101-digit number)
83547532235014419654…15381187314820710401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.670 Γ— 10¹⁰¹(102-digit number)
16709506447002883930…30762374629641420801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.341 Γ— 10¹⁰¹(102-digit number)
33419012894005767861…61524749259282841601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.683 Γ— 10¹⁰¹(102-digit number)
66838025788011535723…23049498518565683201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.336 Γ— 10¹⁰²(103-digit number)
13367605157602307144…46098997037131366401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 586931

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 68e3b0403d5d6f0acdde92d1fad0f20eca4a92fdca1e300380fbb6ab99c16bdc

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 #586,931 on Chainz β†—
Circulating Supply:57,762,721 XPMΒ·at block #6,814,828 Β· updates every 60s
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