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Home/Chain Registry/Block #2,633,815

Block #2,633,815

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 3:11:25 PM Β· Difficulty 11.2091 Β· 4,209,242 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a94ba865e897a87936ea4ee8ee4ff52b7a56d97d8cf797fd21e5949a64cb6202
View on Chainz β†—

Difficulty

11.209134

Transactions

2

Size

575 B

Version

2

Bits

0b3589d4

Nonce

397,148,101

Timestamp

4/28/2018, 3:11:25 PM

Confirmations

4,209,242

Merkle Root

9c4e83edb984efdabbb474ef3f3640ef246bdb5018ac132f580fe5c3092c0990
Transactions (2)
Coinbasecfb0c46a52a364…92f67e0b78fc63
1 in β†’ 1 out7.9600 XPM110 B
Adqah8zh…1WwoHJ9t
adaf64e42cf1f6…2a31084def421e
2 in β†’ 2 out11.9800 XPM375 B
AHSWpUrB…aKSHiDivAbtQ4Qzo…PomZ9hoL
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.

9.358 Γ— 10⁹⁴(95-digit number)
93582127907283058241…20358892072525545280
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
9.358 Γ— 10⁹⁴(95-digit number)
93582127907283058241…20358892072525545281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.871 Γ— 10⁹⁡(96-digit number)
18716425581456611648…40717784145051090561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.743 Γ— 10⁹⁡(96-digit number)
37432851162913223296…81435568290102181121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.486 Γ— 10⁹⁡(96-digit number)
74865702325826446593…62871136580204362241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.497 Γ— 10⁹⁢(97-digit number)
14973140465165289318…25742273160408724481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.994 Γ— 10⁹⁢(97-digit number)
29946280930330578637…51484546320817448961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.989 Γ— 10⁹⁢(97-digit number)
59892561860661157274…02969092641634897921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.197 Γ— 10⁹⁷(98-digit number)
11978512372132231454…05938185283269795841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.395 Γ— 10⁹⁷(98-digit number)
23957024744264462909…11876370566539591681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.791 Γ— 10⁹⁷(98-digit number)
47914049488528925819…23752741133079183361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.582 Γ— 10⁹⁷(98-digit number)
95828098977057851639…47505482266158366721
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 2633815

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 a94ba865e897a87936ea4ee8ee4ff52b7a56d97d8cf797fd21e5949a64cb6202

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 #2,633,815 on Chainz β†—
Circulating Supply:57,988,814 XPMΒ·at block #6,843,056 Β· updates every 60s
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