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Home/Chain Registry/Block #2,635,348

Block #2,635,348

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 5:28:47 AM Β· Difficulty 11.3084 Β· 4,206,969 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
45e4e1ae5aaa36a775c89961ce98e5229c53226cb1a0eabc647a3949cee9031c
View on Chainz β†—

Difficulty

11.308395

Transactions

1

Size

200 B

Version

2

Bits

0b4ef2f3

Nonce

530,839,369

Timestamp

4/29/2018, 5:28:47 AM

Confirmations

4,206,969

Merkle Root

787857fc29a2cfb5e9adf2641acc4b5043a759ca90f821c80dec55b3ff20a7a3
Transactions (1)
Coinbase787857fc29a2cf…ec55b3ff20a7a3
1 in β†’ 1 out7.8100 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.428 Γ— 10⁹⁡(96-digit number)
24285547058150035305…97817590980411875200
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
2.428 Γ— 10⁹⁡(96-digit number)
24285547058150035305…97817590980411875201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.857 Γ— 10⁹⁡(96-digit number)
48571094116300070611…95635181960823750401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.714 Γ— 10⁹⁡(96-digit number)
97142188232600141223…91270363921647500801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.942 Γ— 10⁹⁢(97-digit number)
19428437646520028244…82540727843295001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.885 Γ— 10⁹⁢(97-digit number)
38856875293040056489…65081455686590003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.771 Γ— 10⁹⁢(97-digit number)
77713750586080112979…30162911373180006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.554 Γ— 10⁹⁷(98-digit number)
15542750117216022595…60325822746360012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.108 Γ— 10⁹⁷(98-digit number)
31085500234432045191…20651645492720025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.217 Γ— 10⁹⁷(98-digit number)
62171000468864090383…41303290985440051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.243 Γ— 10⁹⁸(99-digit number)
12434200093772818076…82606581970880102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.486 Γ— 10⁹⁸(99-digit number)
24868400187545636153…65213163941760204801
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 2635348

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 45e4e1ae5aaa36a775c89961ce98e5229c53226cb1a0eabc647a3949cee9031c

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 #2,635,348 on Chainz β†—
Circulating Supply:57,982,944 XPMΒ·at block #6,842,316 Β· updates every 60s
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