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Block #221,964

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/21/2013, 9:27:52 PM Β· Difficulty 9.9399 Β· 6,578,342 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d4a40db1827fb7da183d19320c4ee4816de19251b3779ac53af3b99eea6aff07
View on Chainz β†—

Height

#221,964

Difficulty

9.939865

Transactions

2

Size

865 B

Version

2

Bits

09f09b06

Nonce

22,713

Timestamp

10/21/2013, 9:27:52 PM

Confirmations

6,578,342

Merkle Root

5becc9b6fdf3c318b8a0196a307969ceabd2042f4e68bc05019546a6d84522d6
Transactions (2)
Coinbase186a7184eb5824…994d0e3675b5f3
1 in β†’ 1 out10.1200 XPM109 B
ALL19d7i…aQXE91S4
5beaabf15d2230…88241343295f20
4 in β†’ 2 out332.4503 XPM668 B
AP2bXFfN…B25xHwZuAPB6s3rf…hzd6xuJZ
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.

4.302 Γ— 10⁹⁰(91-digit number)
43021029194835105349…27873276431199234340
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
4.302 Γ— 10⁹⁰(91-digit number)
43021029194835105349…27873276431199234341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.604 Γ— 10⁹⁰(91-digit number)
86042058389670210699…55746552862398468681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.720 Γ— 10⁹¹(92-digit number)
17208411677934042139…11493105724796937361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.441 Γ— 10⁹¹(92-digit number)
34416823355868084279…22986211449593874721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.883 Γ— 10⁹¹(92-digit number)
68833646711736168559…45972422899187749441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.376 Γ— 10⁹²(93-digit number)
13766729342347233711…91944845798375498881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.753 Γ— 10⁹²(93-digit number)
27533458684694467423…83889691596750997761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.506 Γ— 10⁹²(93-digit number)
55066917369388934847…67779383193501995521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.101 Γ— 10⁹³(94-digit number)
11013383473877786969…35558766387003991041
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 221964

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 d4a40db1827fb7da183d19320c4ee4816de19251b3779ac53af3b99eea6aff07

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 #221,964 on Chainz β†—
Circulating Supply:57,646,511 XPMΒ·at block #6,800,305 Β· updates every 60s
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