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Home/Chain Registry/Block #3,241,955

Block #3,241,955

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/26/2019, 3:44:23 PM Β· Difficulty 11.0032 Β· 3,603,284 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b07639728f5bb82909b6ef3e91349c355fe2465447a28cb9d54d33da6fb79991
View on Chainz β†—

Difficulty

11.003222

Transactions

1

Size

200 B

Version

2

Bits

0b00d321

Nonce

296,574,641

Timestamp

6/26/2019, 3:44:23 PM

Confirmations

3,603,284

Merkle Root

15a4d0e685b7e4af673968a96f35bd7334bd8e2582f85fed622baaa67400d36a
Transactions (1)
Coinbase15a4d0e685b7e4…2baaa67400d36a
1 in β†’ 1 out8.2500 XPM110 B
ASiq2qtK…VMhmk7yL
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.

5.688 Γ— 10⁹⁴(95-digit number)
56880637436110992727…68310948042515668640
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
5.688 Γ— 10⁹⁴(95-digit number)
56880637436110992727…68310948042515668639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.137 Γ— 10⁹⁡(96-digit number)
11376127487222198545…36621896085031337279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.275 Γ— 10⁹⁡(96-digit number)
22752254974444397091…73243792170062674559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.550 Γ— 10⁹⁡(96-digit number)
45504509948888794182…46487584340125349119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.100 Γ— 10⁹⁡(96-digit number)
91009019897777588364…92975168680250698239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.820 Γ— 10⁹⁢(97-digit number)
18201803979555517672…85950337360501396479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.640 Γ— 10⁹⁢(97-digit number)
36403607959111035345…71900674721002792959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.280 Γ— 10⁹⁢(97-digit number)
72807215918222070691…43801349442005585919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.456 Γ— 10⁹⁷(98-digit number)
14561443183644414138…87602698884011171839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.912 Γ— 10⁹⁷(98-digit number)
29122886367288828276…75205397768022343679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.824 Γ— 10⁹⁷(98-digit number)
58245772734577656553…50410795536044687359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3241955

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 b07639728f5bb82909b6ef3e91349c355fe2465447a28cb9d54d33da6fb79991

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 #3,241,955 on Chainz β†—
Circulating Supply:58,006,344 XPMΒ·at block #6,845,238 Β· updates every 60s
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