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Block #54,086

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 6:38:09 PM Β· Difficulty 8.9301 Β· 6,772,161 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
91d514bbac1fd7257f5b650917dd79021d3a30b3c4055b9ca2656e0ee3bf05e0
View on Chainz β†—

Height

#54,086

Difficulty

8.930084

Transactions

1

Size

200 B

Version

2

Bits

08ee19f5

Nonce

481

Timestamp

7/16/2013, 6:38:09 PM

Confirmations

6,772,161

Merkle Root

b93043de650a8e0d11e1d5852df68f6c6e92c53c69ef8cdb09af60c7c6c28fe9
Transactions (1)
Coinbaseb93043de650a8e…af60c7c6c28fe9
1 in β†’ 1 out12.5200 XPM110 B
AcBadmkp…GmhL921o
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.

3.509 Γ— 10⁹⁴(95-digit number)
35092451810069250836…46247674036061265560
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
3.509 Γ— 10⁹⁴(95-digit number)
35092451810069250836…46247674036061265559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.018 Γ— 10⁹⁴(95-digit number)
70184903620138501673…92495348072122531119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.403 Γ— 10⁹⁡(96-digit number)
14036980724027700334…84990696144245062239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.807 Γ— 10⁹⁡(96-digit number)
28073961448055400669…69981392288490124479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.614 Γ— 10⁹⁡(96-digit number)
56147922896110801338…39962784576980248959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.122 Γ— 10⁹⁢(97-digit number)
11229584579222160267…79925569153960497919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.245 Γ— 10⁹⁢(97-digit number)
22459169158444320535…59851138307920995839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.491 Γ— 10⁹⁢(97-digit number)
44918338316888641070…19702276615841991679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.983 Γ— 10⁹⁢(97-digit number)
89836676633777282141…39404553231683983359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 54086

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 91d514bbac1fd7257f5b650917dd79021d3a30b3c4055b9ca2656e0ee3bf05e0

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 #54,086 on Chainz β†—
Circulating Supply:57,854,108 XPMΒ·at block #6,826,246 Β· updates every 60s
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