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Block #2,950,500

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/3/2018, 5:11:06 PM Β· Difficulty 11.3966 Β· 3,890,200 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e37ccfba6056533ae50edc6453614ab0eeed2498aa883cfc037883eef3d67842
View on Chainz β†—

Difficulty

11.396636

Transactions

1

Size

200 B

Version

2

Bits

0b6589ef

Nonce

1,583,021,690

Timestamp

12/3/2018, 5:11:06 PM

Confirmations

3,890,200

Merkle Root

2467ac46d991cb3729b3150f43b9004f4e9eac255ade5e765c7b31b2eaac747e
Transactions (1)
Coinbase2467ac46d991cb…7b31b2eaac747e
1 in β†’ 1 out7.6900 XPM110 B
AUhjokok…k5m93PZR
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.

1.326 Γ— 10⁹⁴(95-digit number)
13269597698519101180…41929633634963092240
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
1.326 Γ— 10⁹⁴(95-digit number)
13269597698519101180…41929633634963092241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.653 Γ— 10⁹⁴(95-digit number)
26539195397038202360…83859267269926184481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.307 Γ— 10⁹⁴(95-digit number)
53078390794076404720…67718534539852368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.061 Γ— 10⁹⁡(96-digit number)
10615678158815280944…35437069079704737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.123 Γ— 10⁹⁡(96-digit number)
21231356317630561888…70874138159409475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.246 Γ— 10⁹⁡(96-digit number)
42462712635261123776…41748276318818951681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.492 Γ— 10⁹⁡(96-digit number)
84925425270522247553…83496552637637903361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.698 Γ— 10⁹⁢(97-digit number)
16985085054104449510…66993105275275806721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.397 Γ— 10⁹⁢(97-digit number)
33970170108208899021…33986210550551613441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.794 Γ— 10⁹⁢(97-digit number)
67940340216417798042…67972421101103226881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.358 Γ— 10⁹⁷(98-digit number)
13588068043283559608…35944842202206453761
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 2950500

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 e37ccfba6056533ae50edc6453614ab0eeed2498aa883cfc037883eef3d67842

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 #2,950,500 on Chainz β†—
Circulating Supply:57,969,940 XPMΒ·at block #6,840,699 Β· updates every 60s
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