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Block #22,302

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/12/2013, 4:53:04 PM Β· Difficulty 7.9512 Β· 6,787,478 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7a3b285d2003908617b38f0e0e7e8fed9313d799c9b5d094c363929f16b99d9a
View on Chainz β†—

Height

#22,302

Difficulty

7.951211

Transactions

1

Size

200 B

Version

2

Bits

07f38289

Nonce

316

Timestamp

7/12/2013, 4:53:04 PM

Confirmations

6,787,478

Merkle Root

6795cc01388f6356143f86bd3a4e3691476ab82db45e53ed911a536bb75c09a9
Transactions (1)
Coinbase6795cc01388f63…1a536bb75c09a9
1 in β†’ 1 out15.8000 XPM108 B
Acz8aGVg…JhGrr8ay
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.

2.272 Γ— 10⁹⁹(100-digit number)
22721163160368648296…23542054487370798080
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
2.272 Γ— 10⁹⁹(100-digit number)
22721163160368648296…23542054487370798081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.544 Γ— 10⁹⁹(100-digit number)
45442326320737296592…47084108974741596161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.088 Γ— 10⁹⁹(100-digit number)
90884652641474593184…94168217949483192321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.817 Γ— 10¹⁰⁰(101-digit number)
18176930528294918636…88336435898966384641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.635 Γ— 10¹⁰⁰(101-digit number)
36353861056589837273…76672871797932769281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.270 Γ— 10¹⁰⁰(101-digit number)
72707722113179674547…53345743595865538561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.454 Γ— 10¹⁰¹(102-digit number)
14541544422635934909…06691487191731077121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.908 Γ— 10¹⁰¹(102-digit number)
29083088845271869819…13382974383462154241
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 22302

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 7a3b285d2003908617b38f0e0e7e8fed9313d799c9b5d094c363929f16b99d9a

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 #22,302 on Chainz β†—
Circulating Supply:57,722,319 XPMΒ·at block #6,809,779 Β· updates every 60s
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