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Home/Chain Registry/Block #2,656,806

Block #2,656,806

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/11/2018, 9:34:22 AM Β· Difficulty 11.6838 Β· 4,183,585 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
25564b28608331ac6b35882db753271690161eafdfc09f8c70d04b262f06fc2e
View on Chainz β†—

Difficulty

11.683803

Transactions

1

Size

200 B

Version

2

Bits

0baf0db2

Nonce

974,479,361

Timestamp

5/11/2018, 9:34:22 AM

Confirmations

4,183,585

Merkle Root

e474d487123062b1974f360e143ab4c1a75d2daefc5ec43f09dc9d517f4db1c1
Transactions (1)
Coinbasee474d487123062…dc9d517f4db1c1
1 in β†’ 1 out7.3100 XPM110 B
AJeUGnSX…mi3BiLNw
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.

3.794 Γ— 10⁹⁡(96-digit number)
37949049750011635609…95152796292309021120
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
3.794 Γ— 10⁹⁡(96-digit number)
37949049750011635609…95152796292309021121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.589 Γ— 10⁹⁡(96-digit number)
75898099500023271218…90305592584618042241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.517 Γ— 10⁹⁢(97-digit number)
15179619900004654243…80611185169236084481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.035 Γ— 10⁹⁢(97-digit number)
30359239800009308487…61222370338472168961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.071 Γ— 10⁹⁢(97-digit number)
60718479600018616974…22444740676944337921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.214 Γ— 10⁹⁷(98-digit number)
12143695920003723394…44889481353888675841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.428 Γ— 10⁹⁷(98-digit number)
24287391840007446789…89778962707777351681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.857 Γ— 10⁹⁷(98-digit number)
48574783680014893579…79557925415554703361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.714 Γ— 10⁹⁷(98-digit number)
97149567360029787159…59115850831109406721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.942 Γ— 10⁹⁸(99-digit number)
19429913472005957431…18231701662218813441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.885 Γ— 10⁹⁸(99-digit number)
38859826944011914863…36463403324437626881
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 2656806

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 25564b28608331ac6b35882db753271690161eafdfc09f8c70d04b262f06fc2e

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 #2,656,806 on Chainz β†—
Circulating Supply:57,967,451 XPMΒ·at block #6,840,390 Β· updates every 60s
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