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Home/Chain Registry/Block #2,271,468

Block #2,271,468

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/28/2017, 6:32:54 AM Β· Difficulty 10.9537 Β· 4,572,296 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
12fc5f4a1586733af90bc08a60fa3543c71b23aec3113694cf8e11170aa1d1d7
View on Chainz β†—

Difficulty

10.953731

Transactions

1

Size

197 B

Version

2

Bits

0af427b9

Nonce

2,086,098,697

Timestamp

8/28/2017, 6:32:54 AM

Confirmations

4,572,296

Merkle Root

e6968e8ec4bacc4c1e9326b7bda6a8fb5fca6f653e05ef04030a026a1f63b738
Transactions (1)
Coinbasee6968e8ec4bacc…0a026a1f63b738
1 in β†’ 1 out8.3200 XPM109 B
AbVZAT6p…pCzyk2qr
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.

4.075 Γ— 10⁹⁰(91-digit number)
40758677109112931365…42994269098922317500
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
4.075 Γ— 10⁹⁰(91-digit number)
40758677109112931365…42994269098922317501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.151 Γ— 10⁹⁰(91-digit number)
81517354218225862730…85988538197844635001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.630 Γ— 10⁹¹(92-digit number)
16303470843645172546…71977076395689270001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.260 Γ— 10⁹¹(92-digit number)
32606941687290345092…43954152791378540001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.521 Γ— 10⁹¹(92-digit number)
65213883374580690184…87908305582757080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.304 Γ— 10⁹²(93-digit number)
13042776674916138036…75816611165514160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.608 Γ— 10⁹²(93-digit number)
26085553349832276073…51633222331028320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.217 Γ— 10⁹²(93-digit number)
52171106699664552147…03266444662056640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.043 Γ— 10⁹³(94-digit number)
10434221339932910429…06532889324113280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.086 Γ— 10⁹³(94-digit number)
20868442679865820859…13065778648226560001
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 2271468

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 12fc5f4a1586733af90bc08a60fa3543c71b23aec3113694cf8e11170aa1d1d7

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 #2,271,468 on Chainz β†—
Circulating Supply:57,994,485 XPMΒ·at block #6,843,763 Β· updates every 60s
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