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Block #369,988

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/21/2014, 6:25:53 PM Β· Difficulty 10.4498 Β· 6,428,872 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
014501c9acaf428a52acbcfc0956a53708b53493b24fc292c1f48403e9bd2081
View on Chainz β†—

Height

#369,988

Difficulty

10.449828

Transactions

1

Size

206 B

Version

2

Bits

0a7327ed

Nonce

37,613

Timestamp

1/21/2014, 6:25:53 PM

Confirmations

6,428,872

Merkle Root

fee166188d7939d7903a27680b5fc77163d078aa87f791b6e1b8331b8d4d286c
Transactions (1)
Coinbasefee166188d7939…b8331b8d4d286c
1 in β†’ 1 out9.1400 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.

1.117 Γ— 10⁹⁡(96-digit number)
11176768327467888607…30785089966840135680
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
1.117 Γ— 10⁹⁡(96-digit number)
11176768327467888607…30785089966840135681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.235 Γ— 10⁹⁡(96-digit number)
22353536654935777214…61570179933680271361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.470 Γ— 10⁹⁡(96-digit number)
44707073309871554428…23140359867360542721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.941 Γ— 10⁹⁡(96-digit number)
89414146619743108857…46280719734721085441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.788 Γ— 10⁹⁢(97-digit number)
17882829323948621771…92561439469442170881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.576 Γ— 10⁹⁢(97-digit number)
35765658647897243543…85122878938884341761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.153 Γ— 10⁹⁢(97-digit number)
71531317295794487086…70245757877768683521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.430 Γ— 10⁹⁷(98-digit number)
14306263459158897417…40491515755537367041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.861 Γ— 10⁹⁷(98-digit number)
28612526918317794834…80983031511074734081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.722 Γ— 10⁹⁷(98-digit number)
57225053836635589668…61966063022149468161
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 369988

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 014501c9acaf428a52acbcfc0956a53708b53493b24fc292c1f48403e9bd2081

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 #369,988 on Chainz β†—
Circulating Supply:57,634,915 XPMΒ·at block #6,798,859 Β· updates every 60s
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