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Home/Chain Registry/Block #2,642,657

Block #2,642,657

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 7:43:57 PM Β· Difficulty 11.6599 Β· 4,188,017 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cd2d7ccd5e21392300babba191f50d97859528e152ecdc37b7b55cb4ad387656
View on Chainz β†—

Difficulty

11.659911

Transactions

2

Size

722 B

Version

2

Bits

0ba8eff3

Nonce

221,618,367

Timestamp

5/1/2018, 7:43:57 PM

Confirmations

4,188,017

Merkle Root

e2386327d5ccfb8cdf3f8f91301142004fbe64875a8bea62532a0bc66efac3c0
Transactions (2)
Coinbasea39b9d2094202d…d374c4131033a7
1 in β†’ 1 out7.3500 XPM110 B
Adqah8zh…1WwoHJ9t
8ed4afb75c06d7…43864c15cad99a
3 in β†’ 2 out8.1976 XPM522 B
ATRbm1Hy…wF7mvMGYALFCjDjB…XEfXtzaq
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.

7.880 Γ— 10⁹⁴(95-digit number)
78801309323394030061…68985681706071040000
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
7.880 Γ— 10⁹⁴(95-digit number)
78801309323394030061…68985681706071040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.576 Γ— 10⁹⁡(96-digit number)
15760261864678806012…37971363412142080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.152 Γ— 10⁹⁡(96-digit number)
31520523729357612024…75942726824284160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.304 Γ— 10⁹⁡(96-digit number)
63041047458715224049…51885453648568320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.260 Γ— 10⁹⁢(97-digit number)
12608209491743044809…03770907297136640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.521 Γ— 10⁹⁢(97-digit number)
25216418983486089619…07541814594273280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.043 Γ— 10⁹⁢(97-digit number)
50432837966972179239…15083629188546560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.008 Γ— 10⁹⁷(98-digit number)
10086567593394435847…30167258377093120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.017 Γ— 10⁹⁷(98-digit number)
20173135186788871695…60334516754186240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.034 Γ— 10⁹⁷(98-digit number)
40346270373577743391…20669033508372480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.069 Γ— 10⁹⁷(98-digit number)
80692540747155486782…41338067016744960001
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 2642657

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 cd2d7ccd5e21392300babba191f50d97859528e152ecdc37b7b55cb4ad387656

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 #2,642,657 on Chainz β†—
Circulating Supply:57,889,521 XPMΒ·at block #6,830,673 Β· updates every 60s
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