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Home/Chain Registry/Block #2,070,386

Block #2,070,386

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/14/2017, 5:10:01 AM Β· Difficulty 10.8597 Β· 4,763,472 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
989dfb645a87bb7b9b1513f09c5bab7e2ff52f9dfe428c9bfaa7739a7a161208
View on Chainz β†—

Difficulty

10.859678

Transactions

1

Size

199 B

Version

2

Bits

0adc13d9

Nonce

238,339,849

Timestamp

4/14/2017, 5:10:01 AM

Confirmations

4,763,472

Merkle Root

0ba89a36e1664084816dbc4793e02b880e7f60f9e9ef28ca9c0a8ae938c183c0
Transactions (1)
Coinbase0ba89a36e16640…0a8ae938c183c0
1 in β†’ 1 out8.4700 XPM109 B
ATii2iye…6GWHKLaq
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.

1.565 Γ— 10⁹⁴(95-digit number)
15656683406068987626…77670794827458542900
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
1.565 Γ— 10⁹⁴(95-digit number)
15656683406068987626…77670794827458542899
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.131 Γ— 10⁹⁴(95-digit number)
31313366812137975252…55341589654917085799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.262 Γ— 10⁹⁴(95-digit number)
62626733624275950504…10683179309834171599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.252 Γ— 10⁹⁡(96-digit number)
12525346724855190100…21366358619668343199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.505 Γ— 10⁹⁡(96-digit number)
25050693449710380201…42732717239336686399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.010 Γ— 10⁹⁡(96-digit number)
50101386899420760403…85465434478673372799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁢(97-digit number)
10020277379884152080…70930868957346745599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.004 Γ— 10⁹⁢(97-digit number)
20040554759768304161…41861737914693491199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.008 Γ— 10⁹⁢(97-digit number)
40081109519536608322…83723475829386982399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.016 Γ— 10⁹⁢(97-digit number)
80162219039073216645…67446951658773964799
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 2070386

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 989dfb645a87bb7b9b1513f09c5bab7e2ff52f9dfe428c9bfaa7739a7a161208

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 #2,070,386 on Chainz β†—
Circulating Supply:57,915,093 XPMΒ·at block #6,833,857 Β· updates every 60s
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