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Block #2,638,886

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 10:57:26 AM Β· Difficulty 11.5133 Β· 4,193,874 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
476dd423189a6c24fa1ccfde0678301289d38c5daf9e445747f497daae8981ce
View on Chainz β†—

Difficulty

11.513312

Transactions

1

Size

200 B

Version

2

Bits

0b836866

Nonce

1,727,202,635

Timestamp

4/30/2018, 10:57:26 AM

Confirmations

4,193,874

Merkle Root

8bd1e23e4d22020773d54d33b5f346fd5bb5afd49fec98a77afbb3c5234f523c
Transactions (1)
Coinbase8bd1e23e4d2202…fbb3c5234f523c
1 in β†’ 1 out7.5300 XPM110 B
ASD9Htpb…sBRJZpfT
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.

3.059 Γ— 10⁹⁡(96-digit number)
30594476516994629557…43568560083473160640
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
3.059 Γ— 10⁹⁡(96-digit number)
30594476516994629557…43568560083473160641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.118 Γ— 10⁹⁡(96-digit number)
61188953033989259114…87137120166946321281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.223 Γ— 10⁹⁢(97-digit number)
12237790606797851822…74274240333892642561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.447 Γ— 10⁹⁢(97-digit number)
24475581213595703645…48548480667785285121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.895 Γ— 10⁹⁢(97-digit number)
48951162427191407291…97096961335570570241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.790 Γ— 10⁹⁢(97-digit number)
97902324854382814582…94193922671141140481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.958 Γ— 10⁹⁷(98-digit number)
19580464970876562916…88387845342282280961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.916 Γ— 10⁹⁷(98-digit number)
39160929941753125833…76775690684564561921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.832 Γ— 10⁹⁷(98-digit number)
78321859883506251666…53551381369129123841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.566 Γ— 10⁹⁸(99-digit number)
15664371976701250333…07102762738258247681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.132 Γ— 10⁹⁸(99-digit number)
31328743953402500666…14205525476516495361
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 2638886

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 476dd423189a6c24fa1ccfde0678301289d38c5daf9e445747f497daae8981ce

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 #2,638,886 on Chainz β†—
Circulating Supply:57,906,243 XPMΒ·at block #6,832,759 Β· updates every 60s
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