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Block #386,411

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/2/2014, 11:05:25 AM Β· Difficulty 10.4074 Β· 6,408,347 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
275c5b00d57c3b04823075891a38463c4f4aa61899600d06190826c341664dd5
View on Chainz β†—

Height

#386,411

Difficulty

10.407425

Transactions

2

Size

595 B

Version

2

Bits

0a684d07

Nonce

101,163

Timestamp

2/2/2014, 11:05:25 AM

Confirmations

6,408,347

Merkle Root

6c5c4e9529776d17438d9948195d27c6cdb0469fe3c09c45e7d2561977789ded
Transactions (2)
Coinbaseeb4ef98b6d14b7…09edcf513390f7
1 in β†’ 2 out9.2300 XPM131 B
Ac2JYASP…tcBL5PEWAJno7LX2…vo4wdWtY
9dda9e679d448d…238ac6cf2a2b7c
2 in β†’ 2 out1.4899 XPM374 B
AHsW9kQv…D99YtdEXAKhKN8BS…JNoc2b42
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.

1.293 Γ— 10⁹⁴(95-digit number)
12934225475264135424…85567373437921762600
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
1.293 Γ— 10⁹⁴(95-digit number)
12934225475264135424…85567373437921762601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.586 Γ— 10⁹⁴(95-digit number)
25868450950528270848…71134746875843525201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.173 Γ— 10⁹⁴(95-digit number)
51736901901056541697…42269493751687050401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.034 Γ— 10⁹⁡(96-digit number)
10347380380211308339…84538987503374100801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.069 Γ— 10⁹⁡(96-digit number)
20694760760422616679…69077975006748201601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.138 Γ— 10⁹⁡(96-digit number)
41389521520845233358…38155950013496403201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.277 Γ— 10⁹⁡(96-digit number)
82779043041690466716…76311900026992806401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.655 Γ— 10⁹⁢(97-digit number)
16555808608338093343…52623800053985612801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.311 Γ— 10⁹⁢(97-digit number)
33111617216676186686…05247600107971225601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.622 Γ— 10⁹⁢(97-digit number)
66223234433352373373…10495200215942451201
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 386411

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 275c5b00d57c3b04823075891a38463c4f4aa61899600d06190826c341664dd5

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 #386,411 on Chainz β†—
Circulating Supply:57,602,112 XPMΒ·at block #6,794,757 Β· updates every 60s
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