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Block #221,682

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/21/2013, 5:07:40 PM Β· Difficulty 9.9396 Β· 6,620,199 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f706b50d18e05300cdc3bf274408bcb5d878a9cc1ea71e6a515c41699ee7dba
View on Chainz β†—

Height

#221,682

Difficulty

9.939584

Transactions

2

Size

6.01 KB

Version

2

Bits

09f08890

Nonce

24,122

Timestamp

10/21/2013, 5:07:40 PM

Confirmations

6,620,199

Merkle Root

f55c5920783544c2c19a4e3e55a827ea9c25d0207daef68919f654b1bdb9823d
Transactions (2)
Coinbase2e59f9cdbe2859…8eaf16be76ed2c
1 in β†’ 1 out10.1755 XPM109 B
AUut8t8n…GWEqe1ow
0f11f8d7b3e5bd…9d0bcec4f57d66
40 in β†’ 1 out2.6500 XPM5.82 KB
ASiG7Cav…iYY6J5TU
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.

2.512 Γ— 10⁹⁡(96-digit number)
25121650206606611486…34182194760847593600
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
2.512 Γ— 10⁹⁡(96-digit number)
25121650206606611486…34182194760847593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.024 Γ— 10⁹⁡(96-digit number)
50243300413213222973…68364389521695187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.004 Γ— 10⁹⁢(97-digit number)
10048660082642644594…36728779043390374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.009 Γ— 10⁹⁢(97-digit number)
20097320165285289189…73457558086780748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.019 Γ— 10⁹⁢(97-digit number)
40194640330570578378…46915116173561497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.038 Γ— 10⁹⁢(97-digit number)
80389280661141156756…93830232347122995201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.607 Γ— 10⁹⁷(98-digit number)
16077856132228231351…87660464694245990401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.215 Γ— 10⁹⁷(98-digit number)
32155712264456462702…75320929388491980801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.431 Γ— 10⁹⁷(98-digit number)
64311424528912925405…50641858776983961601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 221682

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 3f706b50d18e05300cdc3bf274408bcb5d878a9cc1ea71e6a515c41699ee7dba

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 #221,682 on Chainz β†—
Circulating Supply:57,979,423 XPMΒ·at block #6,841,880 Β· updates every 60s
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