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Home/Chain Registry/Block #2,294,304

Block #2,294,304

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/13/2017, 5:58:07 AM Β· Difficulty 10.9529 Β· 4,549,340 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cf0de42d0f861842447e7702c1d70717381e3d400ac875a7db8c3fe4d85904ff
View on Chainz β†—

Difficulty

10.952898

Transactions

1

Size

199 B

Version

2

Bits

0af3f126

Nonce

889,017,346

Timestamp

9/13/2017, 5:58:07 AM

Confirmations

4,549,340

Merkle Root

7e7a5262b3a466a9110e897e260210a2f0f5dbaa2bb985a273e15f0a32fba46d
Transactions (1)
Coinbase7e7a5262b3a466…e15f0a32fba46d
1 in β†’ 1 out8.3200 XPM110 B
AHaK6VYA…qPRQDTZ2
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.

3.015 Γ— 10⁹³(94-digit number)
30158152943607070697…76840206025115808010
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
3.015 Γ— 10⁹³(94-digit number)
30158152943607070697…76840206025115808011
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.031 Γ— 10⁹³(94-digit number)
60316305887214141395…53680412050231616021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.206 Γ— 10⁹⁴(95-digit number)
12063261177442828279…07360824100463232041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.412 Γ— 10⁹⁴(95-digit number)
24126522354885656558…14721648200926464081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.825 Γ— 10⁹⁴(95-digit number)
48253044709771313116…29443296401852928161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.650 Γ— 10⁹⁴(95-digit number)
96506089419542626233…58886592803705856321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.930 Γ— 10⁹⁡(96-digit number)
19301217883908525246…17773185607411712641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.860 Γ— 10⁹⁡(96-digit number)
38602435767817050493…35546371214823425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.720 Γ— 10⁹⁡(96-digit number)
77204871535634100986…71092742429646850561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.544 Γ— 10⁹⁢(97-digit number)
15440974307126820197…42185484859293701121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2294304

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 cf0de42d0f861842447e7702c1d70717381e3d400ac875a7db8c3fe4d85904ff

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 #2,294,304 on Chainz β†—
Circulating Supply:57,993,522 XPMΒ·at block #6,843,643 Β· updates every 60s
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