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Block #2,167,504

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/19/2017, 3:02:56 PM Β· Difficulty 10.8984 Β· 4,674,407 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9ee64a366690b920096ef93d78995ed0a58ed8d6d1706612a10db7bce9418e88
View on Chainz β†—

Difficulty

10.898374

Transactions

1

Size

200 B

Version

2

Bits

0ae5fbd0

Nonce

1,348,522,117

Timestamp

6/19/2017, 3:02:56 PM

Confirmations

4,674,407

Merkle Root

c299e69cb4608ad7fa54388ffd5a857e651c1b1791c8ac5979574480bae7636e
Transactions (1)
Coinbasec299e69cb4608a…574480bae7636e
1 in β†’ 1 out8.4100 XPM110 B
ASMd7HDH…De8JrDCL
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.

4.686 Γ— 10⁹⁡(96-digit number)
46868905508029937955…26591199639099490560
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
4.686 Γ— 10⁹⁡(96-digit number)
46868905508029937955…26591199639099490561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.373 Γ— 10⁹⁡(96-digit number)
93737811016059875911…53182399278198981121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.874 Γ— 10⁹⁢(97-digit number)
18747562203211975182…06364798556397962241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.749 Γ— 10⁹⁢(97-digit number)
37495124406423950364…12729597112795924481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.499 Γ— 10⁹⁢(97-digit number)
74990248812847900728…25459194225591848961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.499 Γ— 10⁹⁷(98-digit number)
14998049762569580145…50918388451183697921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.999 Γ— 10⁹⁷(98-digit number)
29996099525139160291…01836776902367395841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.999 Γ— 10⁹⁷(98-digit number)
59992199050278320583…03673553804734791681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.199 Γ— 10⁹⁸(99-digit number)
11998439810055664116…07347107609469583361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.399 Γ— 10⁹⁸(99-digit number)
23996879620111328233…14694215218939166721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.799 Γ— 10⁹⁸(99-digit number)
47993759240222656466…29388430437878333441
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 2167504

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 9ee64a366690b920096ef93d78995ed0a58ed8d6d1706612a10db7bce9418e88

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 #2,167,504 on Chainz β†—
Circulating Supply:57,979,663 XPMΒ·at block #6,841,910 Β· updates every 60s
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