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Home/Chain Registry/Block #2,642,699

Block #2,642,699

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 8:08:23 PM Β· Difficulty 11.6610 Β· 4,202,918 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
96aeb86798937a5a7411746ef6fecc75061ca3475618f4b71c5593d717300d90
View on Chainz β†—

Difficulty

11.661020

Transactions

1

Size

200 B

Version

2

Bits

0ba93897

Nonce

190,289,041

Timestamp

5/1/2018, 8:08:23 PM

Confirmations

4,202,918

Merkle Root

235eaafce79056da7105048bb099e36fbe4e268a792292cc0c9a5613b30f0f62
Transactions (1)
Coinbase235eaafce79056…9a5613b30f0f62
1 in β†’ 1 out7.3400 XPM110 B
ATDAKBu9…GnrkyWmZ
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.

7.020 Γ— 10⁹³(94-digit number)
70201006407673901317…19598824315279703600
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
7.020 Γ— 10⁹³(94-digit number)
70201006407673901317…19598824315279703601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.404 Γ— 10⁹⁴(95-digit number)
14040201281534780263…39197648630559407201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.808 Γ— 10⁹⁴(95-digit number)
28080402563069560526…78395297261118814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.616 Γ— 10⁹⁴(95-digit number)
56160805126139121053…56790594522237628801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.123 Γ— 10⁹⁡(96-digit number)
11232161025227824210…13581189044475257601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.246 Γ— 10⁹⁡(96-digit number)
22464322050455648421…27162378088950515201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.492 Γ— 10⁹⁡(96-digit number)
44928644100911296843…54324756177901030401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.985 Γ— 10⁹⁡(96-digit number)
89857288201822593686…08649512355802060801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.797 Γ— 10⁹⁢(97-digit number)
17971457640364518737…17299024711604121601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.594 Γ— 10⁹⁢(97-digit number)
35942915280729037474…34598049423208243201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.188 Γ— 10⁹⁢(97-digit number)
71885830561458074948…69196098846416486401
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 2642699

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 96aeb86798937a5a7411746ef6fecc75061ca3475618f4b71c5593d717300d90

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 #2,642,699 on Chainz β†—
Circulating Supply:58,009,383 XPMΒ·at block #6,845,616 Β· updates every 60s
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