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Home/Chain Registry/Block #531,873

Block #531,873

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2014, 6:31:35 PM Β· Difficulty 10.8955 Β· 6,294,814 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ad9b30d27b6dd136a21a4268b8fa4c8b0e52f1ff69843511e6d5003531c771a3
View on Chainz β†—

Height

#531,873

Difficulty

10.895461

Transactions

1

Size

208 B

Version

2

Bits

0ae53cf2

Nonce

111,892,522

Timestamp

5/8/2014, 6:31:35 PM

Confirmations

6,294,814

Merkle Root

8417f818d54edf93b1d4f93ebbfe4eae5c4351ad34cc0b3f95b26589a15b65a3
Transactions (1)
Coinbase8417f818d54edf…b26589a15b65a3
1 in β†’ 1 out8.4100 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.

1.242 Γ— 10¹⁰⁰(101-digit number)
12425343930315970168…34219514462460222080
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
1.242 Γ— 10¹⁰⁰(101-digit number)
12425343930315970168…34219514462460222081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.485 Γ— 10¹⁰⁰(101-digit number)
24850687860631940337…68439028924920444161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.970 Γ— 10¹⁰⁰(101-digit number)
49701375721263880675…36878057849840888321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.940 Γ— 10¹⁰⁰(101-digit number)
99402751442527761351…73756115699681776641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.988 Γ— 10¹⁰¹(102-digit number)
19880550288505552270…47512231399363553281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.976 Γ— 10¹⁰¹(102-digit number)
39761100577011104540…95024462798727106561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.952 Γ— 10¹⁰¹(102-digit number)
79522201154022209080…90048925597454213121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.590 Γ— 10¹⁰²(103-digit number)
15904440230804441816…80097851194908426241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.180 Γ— 10¹⁰²(103-digit number)
31808880461608883632…60195702389816852481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.361 Γ— 10¹⁰²(103-digit number)
63617760923217767264…20391404779633704961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.272 Γ— 10¹⁰³(104-digit number)
12723552184643553452…40782809559267409921
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 531873

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 ad9b30d27b6dd136a21a4268b8fa4c8b0e52f1ff69843511e6d5003531c771a3

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 #531,873 on Chainz β†—
Circulating Supply:57,857,646 XPMΒ·at block #6,826,686 Β· updates every 60s
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