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Home/Chain Registry/Block #2,113,652

Block #2,113,652

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/13/2017, 3:19:42 AM Β· Difficulty 10.8993 Β· 4,718,036 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
368365294df43e52c402471bb73e63fd5f8bde27ece8742eaa0efadf21450bd5
View on Chainz β†—

Difficulty

10.899272

Transactions

2

Size

6.05 KB

Version

2

Bits

0ae636b7

Nonce

95,650,506

Timestamp

5/13/2017, 3:19:42 AM

Confirmations

4,718,036

Merkle Root

3d883f16c0a47ea790fdb44fbf275b01c4ce3d057bb7cfd6f82fdbf029a02070
Transactions (2)
Coinbasee9cbb68b3f1d38…c46bcfb9ca4de2
1 in β†’ 1 out8.4900 XPM109 B
APxs1x7F…7BW7jWom
9a08d311c3b6c2…a489250396a7c7
40 in β†’ 2 out200000.0101 XPM5.85 KB
AKAHKtud…mQBq4Q8JAQmvAnkf…nrf9xi8o
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.

1.579 Γ— 10⁹⁴(95-digit number)
15795304144773560614…37592265929113556480
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
1.579 Γ— 10⁹⁴(95-digit number)
15795304144773560614…37592265929113556479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.159 Γ— 10⁹⁴(95-digit number)
31590608289547121228…75184531858227112959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.318 Γ— 10⁹⁴(95-digit number)
63181216579094242457…50369063716454225919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.263 Γ— 10⁹⁡(96-digit number)
12636243315818848491…00738127432908451839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.527 Γ— 10⁹⁡(96-digit number)
25272486631637696983…01476254865816903679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.054 Γ— 10⁹⁡(96-digit number)
50544973263275393966…02952509731633807359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.010 Γ— 10⁹⁢(97-digit number)
10108994652655078793…05905019463267614719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.021 Γ— 10⁹⁢(97-digit number)
20217989305310157586…11810038926535229439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.043 Γ— 10⁹⁢(97-digit number)
40435978610620315172…23620077853070458879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.087 Γ— 10⁹⁢(97-digit number)
80871957221240630345…47240155706140917759
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 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
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 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 2113652

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 368365294df43e52c402471bb73e63fd5f8bde27ece8742eaa0efadf21450bd5

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 #2,113,652 on Chainz β†—
Circulating Supply:57,897,611 XPMΒ·at block #6,831,687 Β· updates every 60s
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