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Home/Chain Registry/Block #2,657,533

Block #2,657,533

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/12/2018, 2:07:29 AM Β· Difficulty 11.6667 Β· 4,185,489 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cecbf7c6bc55491ca48fd08dd2356b988b3617d7773ae038b0c318d814084c44
View on Chainz β†—

Difficulty

11.666746

Transactions

1

Size

199 B

Version

2

Bits

0baaafe5

Nonce

655,668,569

Timestamp

5/12/2018, 2:07:29 AM

Confirmations

4,185,489

Merkle Root

080c9db1033e7dee043fa38e412d55af7cdba120c34348c910bd90df2e7e44d4
Transactions (1)
Coinbase080c9db1033e7d…bd90df2e7e44d4
1 in β†’ 1 out7.3300 XPM109 B
ActruxdH…1pX9DYbs
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.

1.062 Γ— 10⁹⁡(96-digit number)
10628443904529384670…46041769850521837920
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
1.062 Γ— 10⁹⁡(96-digit number)
10628443904529384670…46041769850521837921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.125 Γ— 10⁹⁡(96-digit number)
21256887809058769340…92083539701043675841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.251 Γ— 10⁹⁡(96-digit number)
42513775618117538681…84167079402087351681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.502 Γ— 10⁹⁡(96-digit number)
85027551236235077363…68334158804174703361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.700 Γ— 10⁹⁢(97-digit number)
17005510247247015472…36668317608349406721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.401 Γ— 10⁹⁢(97-digit number)
34011020494494030945…73336635216698813441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.802 Γ— 10⁹⁢(97-digit number)
68022040988988061890…46673270433397626881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.360 Γ— 10⁹⁷(98-digit number)
13604408197797612378…93346540866795253761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.720 Γ— 10⁹⁷(98-digit number)
27208816395595224756…86693081733590507521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.441 Γ— 10⁹⁷(98-digit number)
54417632791190449512…73386163467181015041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.088 Γ— 10⁹⁸(99-digit number)
10883526558238089902…46772326934362030081
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 2657533

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 cecbf7c6bc55491ca48fd08dd2356b988b3617d7773ae038b0c318d814084c44

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 #2,657,533 on Chainz β†—
Circulating Supply:57,988,532 XPMΒ·at block #6,843,021 Β· updates every 60s
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