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Home/Chain Registry/Block #339,972

Block #339,972

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/2/2014, 11:42:25 AM Β· Difficulty 10.1274 Β· 6,471,864 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b300c72a7df1a75c1f9b21cf4aba216cefac5e16e22d1644d78e596c059dc29e
View on Chainz β†—

Height

#339,972

Difficulty

10.127359

Transactions

1

Size

206 B

Version

2

Bits

0a209aa0

Nonce

469,763,688

Timestamp

1/2/2014, 11:42:25 AM

Confirmations

6,471,864

Merkle Root

612ac5769fe52d229917046d3036cd7ecef828798fa0e189b7768d42c4c4ee5b
Transactions (1)
Coinbase612ac5769fe52d…768d42c4c4ee5b
1 in β†’ 1 out9.7400 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.

5.399 Γ— 10⁹⁡(96-digit number)
53995907605981040594…83719954422382694160
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.399 Γ— 10⁹⁡(96-digit number)
53995907605981040594…83719954422382694159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.079 Γ— 10⁹⁢(97-digit number)
10799181521196208118…67439908844765388319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.159 Γ— 10⁹⁢(97-digit number)
21598363042392416237…34879817689530776639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.319 Γ— 10⁹⁢(97-digit number)
43196726084784832475…69759635379061553279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.639 Γ— 10⁹⁢(97-digit number)
86393452169569664951…39519270758123106559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.727 Γ— 10⁹⁷(98-digit number)
17278690433913932990…79038541516246213119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.455 Γ— 10⁹⁷(98-digit number)
34557380867827865980…58077083032492426239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.911 Γ— 10⁹⁷(98-digit number)
69114761735655731961…16154166064984852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁸(99-digit number)
13822952347131146392…32308332129969704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.764 Γ— 10⁹⁸(99-digit number)
27645904694262292784…64616664259939409919
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 339972

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 b300c72a7df1a75c1f9b21cf4aba216cefac5e16e22d1644d78e596c059dc29e

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 #339,972 on Chainz β†—
Circulating Supply:57,738,789 XPMΒ·at block #6,811,835 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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