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Home/Chain Registry/Block #2,020,663

Block #2,020,663

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/13/2017, 2:57:33 AM Β· Difficulty 10.7145 Β· 4,810,262 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
002cd2973b2ebf5e66e8f6e95184fc35e5547b7b7f3d454fc1bf978581949a06
View on Chainz β†—

Difficulty

10.714457

Transactions

1

Size

199 B

Version

2

Bits

0ab6e6a2

Nonce

1,250,306,527

Timestamp

3/13/2017, 2:57:33 AM

Confirmations

4,810,262

Merkle Root

5e232f406e90e140bad8b13db4daa779d96531bce5f2fe97dc9e362365e74545
Transactions (1)
Coinbase5e232f406e90e1…9e362365e74545
1 in β†’ 1 out8.7000 XPM109 B
AM2BTpyX…cjimfX3U
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.

5.315 Γ— 10⁹⁴(95-digit number)
53153463122189070772…26571285803514093760
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
5.315 Γ— 10⁹⁴(95-digit number)
53153463122189070772…26571285803514093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.063 Γ— 10⁹⁡(96-digit number)
10630692624437814154…53142571607028187521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.126 Γ— 10⁹⁡(96-digit number)
21261385248875628309…06285143214056375041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.252 Γ— 10⁹⁡(96-digit number)
42522770497751256618…12570286428112750081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.504 Γ— 10⁹⁡(96-digit number)
85045540995502513236…25140572856225500161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.700 Γ— 10⁹⁢(97-digit number)
17009108199100502647…50281145712451000321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.401 Γ— 10⁹⁢(97-digit number)
34018216398201005294…00562291424902000641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.803 Γ— 10⁹⁢(97-digit number)
68036432796402010589…01124582849804001281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.360 Γ— 10⁹⁷(98-digit number)
13607286559280402117…02249165699608002561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.721 Γ— 10⁹⁷(98-digit number)
27214573118560804235…04498331399216005121
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 2020663

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 002cd2973b2ebf5e66e8f6e95184fc35e5547b7b7f3d454fc1bf978581949a06

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 #2,020,663 on Chainz β†—
Circulating Supply:57,891,531 XPMΒ·at block #6,830,924 Β· updates every 60s
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