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Home/Chain Registry/Block #2,635,076

Block #2,635,076

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 3:07:17 AM Β· Difficulty 11.2902 Β· 4,196,548 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
03fbdf98a2dabcb2d26007ee24f2bce1b7f9a6d233c2178da6d32dffcd9dc109
View on Chainz β†—

Difficulty

11.290231

Transactions

1

Size

199 B

Version

2

Bits

0b4a4c95

Nonce

518,066,325

Timestamp

4/29/2018, 3:07:17 AM

Confirmations

4,196,548

Merkle Root

afb7c53764fc0e94bc0d428a5c0a4162d40df4fc7a2f9b1bdc6242cf99a85d72
Transactions (1)
Coinbaseafb7c53764fc0e…6242cf99a85d72
1 in β†’ 1 out7.8300 XPM110 B
AViddRso…giUMYUok
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.

2.526 Γ— 10⁹²(93-digit number)
25266323604505688045…29860692003602966800
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
2.526 Γ— 10⁹²(93-digit number)
25266323604505688045…29860692003602966801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.053 Γ— 10⁹²(93-digit number)
50532647209011376091…59721384007205933601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.010 Γ— 10⁹³(94-digit number)
10106529441802275218…19442768014411867201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.021 Γ— 10⁹³(94-digit number)
20213058883604550436…38885536028823734401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.042 Γ— 10⁹³(94-digit number)
40426117767209100873…77771072057647468801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.085 Γ— 10⁹³(94-digit number)
80852235534418201746…55542144115294937601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.617 Γ— 10⁹⁴(95-digit number)
16170447106883640349…11084288230589875201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.234 Γ— 10⁹⁴(95-digit number)
32340894213767280698…22168576461179750401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.468 Γ— 10⁹⁴(95-digit number)
64681788427534561396…44337152922359500801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.293 Γ— 10⁹⁡(96-digit number)
12936357685506912279…88674305844719001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.587 Γ— 10⁹⁡(96-digit number)
25872715371013824558…77348611689438003201
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 2635076

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 03fbdf98a2dabcb2d26007ee24f2bce1b7f9a6d233c2178da6d32dffcd9dc109

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 #2,635,076 on Chainz β†—
Circulating Supply:57,897,093 XPMΒ·at block #6,831,623 Β· updates every 60s
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