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Block #2,638,647

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 8:50:10 AM Β· Difficulty 11.5024 Β· 4,202,895 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e6537c73b4b359928d9d5eed2121d539888164432ec8096922e47b28ee96f2c2
View on Chainz β†—

Difficulty

11.502421

Transactions

1

Size

200 B

Version

2

Bits

0b809eac

Nonce

113,637,991

Timestamp

4/30/2018, 8:50:10 AM

Confirmations

4,202,895

Merkle Root

75671150b4cbdf38bc267f4f08006aec77bf5da025718bafd90913461ab2a6ee
Transactions (1)
Coinbase75671150b4cbdf…0913461ab2a6ee
1 in β†’ 1 out7.5500 XPM110 B
AXxpnN14…tGseb8EX
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.

1.880 Γ— 10⁹⁡(96-digit number)
18801938718695586536…43372030304635463360
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
1.880 Γ— 10⁹⁡(96-digit number)
18801938718695586536…43372030304635463361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.760 Γ— 10⁹⁡(96-digit number)
37603877437391173072…86744060609270926721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.520 Γ— 10⁹⁡(96-digit number)
75207754874782346144…73488121218541853441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.504 Γ— 10⁹⁢(97-digit number)
15041550974956469228…46976242437083706881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.008 Γ— 10⁹⁢(97-digit number)
30083101949912938457…93952484874167413761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.016 Γ— 10⁹⁢(97-digit number)
60166203899825876915…87904969748334827521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.203 Γ— 10⁹⁷(98-digit number)
12033240779965175383…75809939496669655041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.406 Γ— 10⁹⁷(98-digit number)
24066481559930350766…51619878993339310081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.813 Γ— 10⁹⁷(98-digit number)
48132963119860701532…03239757986678620161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.626 Γ— 10⁹⁷(98-digit number)
96265926239721403065…06479515973357240321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.925 Γ— 10⁹⁸(99-digit number)
19253185247944280613…12959031946714480641
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 2638647

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 e6537c73b4b359928d9d5eed2121d539888164432ec8096922e47b28ee96f2c2

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 #2,638,647 on Chainz β†—
Circulating Supply:57,976,718 XPMΒ·at block #6,841,541 Β· updates every 60s
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