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Home/Chain Registry/Block #301,566

Block #301,566

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/9/2013, 6:58:47 AM Β· Difficulty 9.9925 Β· 6,497,343 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7da600c60ffb030ff29f519c8723b210c4854550cfe051ea8a1af7c1a9a5f63b
View on Chainz β†—

Height

#301,566

Difficulty

9.992532

Transactions

1

Size

207 B

Version

2

Bits

09fe1692

Nonce

107,080

Timestamp

12/9/2013, 6:58:47 AM

Confirmations

6,497,343

Merkle Root

875128eb40b8bc1ae2782b98a24b74aa3a23ee3d6dc362097b239190541db30c
Transactions (1)
Coinbase875128eb40b8bc…239190541db30c
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

5.091 Γ— 10⁹⁢(97-digit number)
50914037196836532870…16835000355172666690
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
5.091 Γ— 10⁹⁢(97-digit number)
50914037196836532870…16835000355172666691
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.018 Γ— 10⁹⁷(98-digit number)
10182807439367306574…33670000710345333381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.036 Γ— 10⁹⁷(98-digit number)
20365614878734613148…67340001420690666761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.073 Γ— 10⁹⁷(98-digit number)
40731229757469226296…34680002841381333521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.146 Γ— 10⁹⁷(98-digit number)
81462459514938452593…69360005682762667041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.629 Γ— 10⁹⁸(99-digit number)
16292491902987690518…38720011365525334081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.258 Γ— 10⁹⁸(99-digit number)
32584983805975381037…77440022731050668161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.516 Γ— 10⁹⁸(99-digit number)
65169967611950762074…54880045462101336321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.303 Γ— 10⁹⁹(100-digit number)
13033993522390152414…09760090924202672641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.606 Γ— 10⁹⁹(100-digit number)
26067987044780304829…19520181848405345281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 301566

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 7da600c60ffb030ff29f519c8723b210c4854550cfe051ea8a1af7c1a9a5f63b

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 #301,566 on Chainz β†—
Circulating Supply:57,635,312 XPMΒ·at block #6,798,908 Β· updates every 60s
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