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Home/Chain Registry/Block #2,640,083

Block #2,640,083

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 9:13:56 PM Β· Difficulty 11.5662 Β· 4,192,915 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
03ce2d7ed0f6b228a2291c84ee5f3e01853b3f0ddf615961a3dcb6976edece0c
View on Chainz β†—

Difficulty

11.566209

Transactions

1

Size

199 B

Version

2

Bits

0b90f318

Nonce

391,601,134

Timestamp

4/30/2018, 9:13:56 PM

Confirmations

4,192,915

Merkle Root

3f13dc9590b5660ef8985b153a489abccbfdde568db028c37455542a84b8f747
Transactions (1)
Coinbase3f13dc9590b566…55542a84b8f747
1 in β†’ 1 out7.4600 XPM110 B
AHkQzcfJ…qcGiaQxk
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.

9.785 Γ— 10⁹²(93-digit number)
97853639724277838748…68701177370391966720
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
9.785 Γ— 10⁹²(93-digit number)
97853639724277838748…68701177370391966721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.957 Γ— 10⁹³(94-digit number)
19570727944855567749…37402354740783933441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.914 Γ— 10⁹³(94-digit number)
39141455889711135499…74804709481567866881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.828 Γ— 10⁹³(94-digit number)
78282911779422270999…49609418963135733761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.565 Γ— 10⁹⁴(95-digit number)
15656582355884454199…99218837926271467521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.131 Γ— 10⁹⁴(95-digit number)
31313164711768908399…98437675852542935041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.262 Γ— 10⁹⁴(95-digit number)
62626329423537816799…96875351705085870081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.252 Γ— 10⁹⁡(96-digit number)
12525265884707563359…93750703410171740161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.505 Γ— 10⁹⁡(96-digit number)
25050531769415126719…87501406820343480321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.010 Γ— 10⁹⁡(96-digit number)
50101063538830253439…75002813640686960641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.002 Γ— 10⁹⁢(97-digit number)
10020212707766050687…50005627281373921281
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 2640083

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 03ce2d7ed0f6b228a2291c84ee5f3e01853b3f0ddf615961a3dcb6976edece0c

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 #2,640,083 on Chainz β†—
Circulating Supply:57,908,156 XPMΒ·at block #6,832,997 Β· updates every 60s
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