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Home/Chain Registry/Block #332,986

Block #332,986

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/28/2013, 11:11:22 AM Β· Difficulty 10.1656 Β· 6,498,275 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
78f9b6dc1075517caae73ba74d10d0f816be967fab9279ecc26cd93643c6c6aa
View on Chainz β†—

Height

#332,986

Difficulty

10.165616

Transactions

1

Size

207 B

Version

2

Bits

0a2a65d7

Nonce

55,398

Timestamp

12/28/2013, 11:11:22 AM

Confirmations

6,498,275

Merkle Root

ad3cc026334421c4eaae75f95ed86850a6918078a41bc6d7d36e3dfaa25a6c2e
Transactions (1)
Coinbasead3cc026334421…6e3dfaa25a6c2e
1 in β†’ 1 out9.6600 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.

5.187 Γ— 10⁹⁢(97-digit number)
51875221302600039520…88633052924187269400
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
5.187 Γ— 10⁹⁢(97-digit number)
51875221302600039520…88633052924187269401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.037 Γ— 10⁹⁷(98-digit number)
10375044260520007904…77266105848374538801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.075 Γ— 10⁹⁷(98-digit number)
20750088521040015808…54532211696749077601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.150 Γ— 10⁹⁷(98-digit number)
41500177042080031616…09064423393498155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.300 Γ— 10⁹⁷(98-digit number)
83000354084160063232…18128846786996310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.660 Γ— 10⁹⁸(99-digit number)
16600070816832012646…36257693573992620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.320 Γ— 10⁹⁸(99-digit number)
33200141633664025293…72515387147985241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.640 Γ— 10⁹⁸(99-digit number)
66400283267328050586…45030774295970483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.328 Γ— 10⁹⁹(100-digit number)
13280056653465610117…90061548591940966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.656 Γ— 10⁹⁹(100-digit number)
26560113306931220234…80123097183881932801
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 332986

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 78f9b6dc1075517caae73ba74d10d0f816be967fab9279ecc26cd93643c6c6aa

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 #332,986 on Chainz β†—
Circulating Supply:57,894,239 XPMΒ·at block #6,831,260 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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