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Block #1,586,468

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2016, 2:10:24 AM Β· Difficulty 10.6500 Β· 5,226,244 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e84d2d4f3d38659b2cb3863cc2f59f5c3b6f193ec8fd8984c9a4bc1d838dc9d
View on Chainz β†—

Difficulty

10.649977

Transactions

1

Size

199 B

Version

2

Bits

0aa664eb

Nonce

1,326,432,947

Timestamp

5/16/2016, 2:10:24 AM

Confirmations

5,226,244

Merkle Root

c9545ba1ec63e44874dcabd9cbb33e33556811ca933cc509d1a6eea31b9063a5
Transactions (1)
Coinbasec9545ba1ec63e4…a6eea31b9063a5
1 in β†’ 1 out8.8000 XPM109 B
AZ6Qbe4e…YZCsneyk
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.

1.151 Γ— 10⁹⁴(95-digit number)
11518628382998164162…70753869175505176660
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
1.151 Γ— 10⁹⁴(95-digit number)
11518628382998164162…70753869175505176661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.303 Γ— 10⁹⁴(95-digit number)
23037256765996328325…41507738351010353321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.607 Γ— 10⁹⁴(95-digit number)
46074513531992656651…83015476702020706641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.214 Γ— 10⁹⁴(95-digit number)
92149027063985313302…66030953404041413281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.842 Γ— 10⁹⁡(96-digit number)
18429805412797062660…32061906808082826561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.685 Γ— 10⁹⁡(96-digit number)
36859610825594125321…64123813616165653121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.371 Γ— 10⁹⁡(96-digit number)
73719221651188250642…28247627232331306241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.474 Γ— 10⁹⁢(97-digit number)
14743844330237650128…56495254464662612481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.948 Γ— 10⁹⁢(97-digit number)
29487688660475300256…12990508929325224961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.897 Γ— 10⁹⁢(97-digit number)
58975377320950600513…25981017858650449921
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 1586468

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 7e84d2d4f3d38659b2cb3863cc2f59f5c3b6f193ec8fd8984c9a4bc1d838dc9d

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 #1,586,468 on Chainz β†—
Circulating Supply:57,745,734 XPMΒ·at block #6,812,711 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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