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Block #221,885

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/21/2013, 8:14:27 PM Β· Difficulty 9.9398 Β· 6,603,583 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9d213c28bccd36cdd7d044365901416c4f2374c7190e9dd2d134d8b5ff9f607a
View on Chainz β†—

Height

#221,885

Difficulty

9.939787

Transactions

1

Size

200 B

Version

2

Bits

09f095dd

Nonce

67,901

Timestamp

10/21/2013, 8:14:27 PM

Confirmations

6,603,583

Merkle Root

c0631eb327f30f52f93a0cfc504f73692a8643bf6edfd48aa0f33478a5818465
Transactions (1)
Coinbasec0631eb327f30f…f33478a5818465
1 in β†’ 1 out10.1100 XPM109 B
AbkHsEj8…KxpskbJZ
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.

3.149 Γ— 10⁹⁢(97-digit number)
31491946393918262224…67764461802329339520
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
3.149 Γ— 10⁹⁢(97-digit number)
31491946393918262224…67764461802329339521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.298 Γ— 10⁹⁢(97-digit number)
62983892787836524448…35528923604658679041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.259 Γ— 10⁹⁷(98-digit number)
12596778557567304889…71057847209317358081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.519 Γ— 10⁹⁷(98-digit number)
25193557115134609779…42115694418634716161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.038 Γ— 10⁹⁷(98-digit number)
50387114230269219558…84231388837269432321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.007 Γ— 10⁹⁸(99-digit number)
10077422846053843911…68462777674538864641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.015 Γ— 10⁹⁸(99-digit number)
20154845692107687823…36925555349077729281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.030 Γ— 10⁹⁸(99-digit number)
40309691384215375646…73851110698155458561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.061 Γ— 10⁹⁸(99-digit number)
80619382768430751293…47702221396310917121
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 221885

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 9d213c28bccd36cdd7d044365901416c4f2374c7190e9dd2d134d8b5ff9f607a

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 #221,885 on Chainz β†—
Circulating Supply:57,847,836 XPMΒ·at block #6,825,467 Β· updates every 60s
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