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Home/Chain Registry/Block #2,314,880

Block #2,314,880

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2017, 10:49:13 PM Β· Difficulty 10.9070 Β· 4,530,462 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dd3aa86d665435e9ad044eb2947f21241c78bbc587ffff4c1991842468a87675
View on Chainz β†—

Difficulty

10.906955

Transactions

1

Size

200 B

Version

2

Bits

0ae82e35

Nonce

852,974,053

Timestamp

9/29/2017, 10:49:13 PM

Confirmations

4,530,462

Merkle Root

25e1c1f4c5d8ec337d4ccd491ed7fb4c95ec1962a8ced230625e1c9f655ac9aa
Transactions (1)
Coinbase25e1c1f4c5d8ec…5e1c9f655ac9aa
1 in β†’ 1 out8.3900 XPM110 B
AWf1nLT7…1XVZAddE
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.

1.351 Γ— 10⁹⁴(95-digit number)
13511589055220642449…42538055820967729920
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
1.351 Γ— 10⁹⁴(95-digit number)
13511589055220642449…42538055820967729921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.702 Γ— 10⁹⁴(95-digit number)
27023178110441284899…85076111641935459841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.404 Γ— 10⁹⁴(95-digit number)
54046356220882569798…70152223283870919681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.080 Γ— 10⁹⁡(96-digit number)
10809271244176513959…40304446567741839361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.161 Γ— 10⁹⁡(96-digit number)
21618542488353027919…80608893135483678721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.323 Γ— 10⁹⁡(96-digit number)
43237084976706055839…61217786270967357441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.647 Γ— 10⁹⁡(96-digit number)
86474169953412111678…22435572541934714881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.729 Γ— 10⁹⁢(97-digit number)
17294833990682422335…44871145083869429761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.458 Γ— 10⁹⁢(97-digit number)
34589667981364844671…89742290167738859521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.917 Γ— 10⁹⁢(97-digit number)
69179335962729689342…79484580335477719041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.383 Γ— 10⁹⁷(98-digit number)
13835867192545937868…58969160670955438081
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 2314880

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 dd3aa86d665435e9ad044eb2947f21241c78bbc587ffff4c1991842468a87675

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 #2,314,880 on Chainz β†—
Circulating Supply:58,007,177 XPMΒ·at block #6,845,341 Β· updates every 60s
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