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Home/Chain Registry/Block #2,118,466

Block #2,118,466

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2017, 3:35:27 AM Β· Difficulty 10.9085 Β· 4,714,418 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
be17e752a6e5548cc86c9fe3238e380795a5f31c49d3315ac2add9ec265a20d9
View on Chainz β†—

Difficulty

10.908525

Transactions

1

Size

208 B

Version

2

Bits

0ae8951b

Nonce

128,200,420

Timestamp

5/16/2017, 3:35:27 AM

Confirmations

4,714,418

Merkle Root

a8efe7e07a49fce592559e1a133fb7266293492e2bbb2c5a01e6092578cc5537
Transactions (1)
Coinbasea8efe7e07a49fc…e6092578cc5537
1 in β†’ 1 out8.3900 XPM118 B
AM6GYpjw…aw86QDtR
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.

1.706 Γ— 10⁹⁡(96-digit number)
17060366104716720057…66266867169401830400
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
1.706 Γ— 10⁹⁡(96-digit number)
17060366104716720057…66266867169401830401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.412 Γ— 10⁹⁡(96-digit number)
34120732209433440115…32533734338803660801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.824 Γ— 10⁹⁡(96-digit number)
68241464418866880231…65067468677607321601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.364 Γ— 10⁹⁢(97-digit number)
13648292883773376046…30134937355214643201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.729 Γ— 10⁹⁢(97-digit number)
27296585767546752092…60269874710429286401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.459 Γ— 10⁹⁢(97-digit number)
54593171535093504185…20539749420858572801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.091 Γ— 10⁹⁷(98-digit number)
10918634307018700837…41079498841717145601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.183 Γ— 10⁹⁷(98-digit number)
21837268614037401674…82158997683434291201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.367 Γ— 10⁹⁷(98-digit number)
43674537228074803348…64317995366868582401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.734 Γ— 10⁹⁷(98-digit number)
87349074456149606696…28635990733737164801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.746 Γ— 10⁹⁸(99-digit number)
17469814891229921339…57271981467474329601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
3.493 Γ— 10⁹⁸(99-digit number)
34939629782459842678…14543962934948659201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2118466

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 be17e752a6e5548cc86c9fe3238e380795a5f31c49d3315ac2add9ec265a20d9

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 #2,118,466 on Chainz β†—
Circulating Supply:57,907,241 XPMΒ·at block #6,832,883 Β· updates every 60s
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