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Home/Chain Registry/Block #2,114,540

Block #2,114,540

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/13/2017, 5:16:10 PM Β· Difficulty 10.9003 Β· 4,728,303 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6db302ce1f9920d5a636a27d61e5a68c2b8d097c3896424e55c2d34b8ae7b700
View on Chainz β†—

Difficulty

10.900325

Transactions

1

Size

198 B

Version

2

Bits

0ae67bb7

Nonce

49,831,165

Timestamp

5/13/2017, 5:16:10 PM

Confirmations

4,728,303

Merkle Root

e01119a2087f9d0c4b08d266d383ac57ddfc471f88c6226ce0c9aedf4944c04c
Transactions (1)
Coinbasee01119a2087f9d…c9aedf4944c04c
1 in β†’ 1 out8.4000 XPM109 B
AHmynMXC…hufiZsHK
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.

2.818 Γ— 10⁹²(93-digit number)
28188967160249969524…87785807137027578240
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.818 Γ— 10⁹²(93-digit number)
28188967160249969524…87785807137027578239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.637 Γ— 10⁹²(93-digit number)
56377934320499939049…75571614274055156479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.127 Γ— 10⁹³(94-digit number)
11275586864099987809…51143228548110312959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.255 Γ— 10⁹³(94-digit number)
22551173728199975619…02286457096220625919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.510 Γ— 10⁹³(94-digit number)
45102347456399951239…04572914192441251839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.020 Γ— 10⁹³(94-digit number)
90204694912799902479…09145828384882503679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.804 Γ— 10⁹⁴(95-digit number)
18040938982559980495…18291656769765007359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.608 Γ— 10⁹⁴(95-digit number)
36081877965119960991…36583313539530014719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.216 Γ— 10⁹⁴(95-digit number)
72163755930239921983…73166627079060029439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.443 Γ— 10⁹⁡(96-digit number)
14432751186047984396…46333254158120058879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.886 Γ— 10⁹⁡(96-digit number)
28865502372095968793…92666508316240117759
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2114540

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 6db302ce1f9920d5a636a27d61e5a68c2b8d097c3896424e55c2d34b8ae7b700

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 #2,114,540 on Chainz β†—
Circulating Supply:57,987,088 XPMΒ·at block #6,842,842 Β· updates every 60s
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