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Block #220,088

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/20/2013, 8:07:43 PM Β· Difficulty 9.9354 Β· 6,575,948 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ff0b2041c67a5ad3bbc03422c337d91ade8837eaf59b4839cda62f7aa71128f
View on Chainz β†—

Height

#220,088

Difficulty

9.935355

Transactions

1

Size

206 B

Version

2

Bits

09ef736c

Nonce

11,538

Timestamp

10/20/2013, 8:07:43 PM

Confirmations

6,575,948

Merkle Root

b744aff5173f6f862d41c5721730fdf5df9fb1529e14cc34b13091068bc90976
Transactions (1)
Coinbaseb744aff5173f6f…3091068bc90976
1 in β†’ 1 out10.1200 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.888 Γ— 10⁹⁴(95-digit number)
48881789483559660671…26133612017398134360
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
4.888 Γ— 10⁹⁴(95-digit number)
48881789483559660671…26133612017398134361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.776 Γ— 10⁹⁴(95-digit number)
97763578967119321342…52267224034796268721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.955 Γ— 10⁹⁡(96-digit number)
19552715793423864268…04534448069592537441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.910 Γ— 10⁹⁡(96-digit number)
39105431586847728536…09068896139185074881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.821 Γ— 10⁹⁡(96-digit number)
78210863173695457073…18137792278370149761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.564 Γ— 10⁹⁢(97-digit number)
15642172634739091414…36275584556740299521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.128 Γ— 10⁹⁢(97-digit number)
31284345269478182829…72551169113480599041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.256 Γ— 10⁹⁢(97-digit number)
62568690538956365659…45102338226961198081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.251 Γ— 10⁹⁷(98-digit number)
12513738107791273131…90204676453922396161
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 220088

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 6ff0b2041c67a5ad3bbc03422c337d91ade8837eaf59b4839cda62f7aa71128f

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 #220,088 on Chainz β†—
Circulating Supply:57,612,380 XPMΒ·at block #6,796,035 Β· updates every 60s
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