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Home/Chain Registry/Block #2,633,498

Block #2,633,498

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 11:32:57 AM Β· Difficulty 11.1936 Β· 4,199,619 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a5051e76c86028b53b83d08bddb26c1a978f64fc26bb992ca951fe4c75ceef2
View on Chainz β†—

Difficulty

11.193633

Transactions

1

Size

201 B

Version

2

Bits

0b3191e8

Nonce

242,273,530

Timestamp

4/28/2018, 11:32:57 AM

Confirmations

4,199,619

Merkle Root

cfd013e2ee3ff13186592ece32299168d304b7b832f3afa6326b46da5ed47df5
Transactions (1)
Coinbasecfd013e2ee3ff1…6b46da5ed47df5
1 in β†’ 1 out7.9700 XPM110 B
ANJgn7Fg…hmsCxS16
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.

1.501 Γ— 10⁹⁷(98-digit number)
15012528395109078854…57628533550789212160
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
1.501 Γ— 10⁹⁷(98-digit number)
15012528395109078854…57628533550789212161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.002 Γ— 10⁹⁷(98-digit number)
30025056790218157708…15257067101578424321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.005 Γ— 10⁹⁷(98-digit number)
60050113580436315417…30514134203156848641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.201 Γ— 10⁹⁸(99-digit number)
12010022716087263083…61028268406313697281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.402 Γ— 10⁹⁸(99-digit number)
24020045432174526166…22056536812627394561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.804 Γ— 10⁹⁸(99-digit number)
48040090864349052333…44113073625254789121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.608 Γ— 10⁹⁸(99-digit number)
96080181728698104667…88226147250509578241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.921 Γ— 10⁹⁹(100-digit number)
19216036345739620933…76452294501019156481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.843 Γ— 10⁹⁹(100-digit number)
38432072691479241867…52904589002038312961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.686 Γ— 10⁹⁹(100-digit number)
76864145382958483734…05809178004076625921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.537 Γ— 10¹⁰⁰(101-digit number)
15372829076591696746…11618356008153251841
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 2633498

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 5a5051e76c86028b53b83d08bddb26c1a978f64fc26bb992ca951fe4c75ceef2

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 #2,633,498 on Chainz β†—
Circulating Supply:57,909,111 XPMΒ·at block #6,833,116 Β· updates every 60s
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