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Home/Chain Registry/Block #3,364,739

Block #3,364,739

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/22/2019, 7:58:26 AM Β· Difficulty 10.9954 Β· 3,468,588 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f239b333eb80b4e10d8de6b75862ff3480f344b7c403c99318dc92ba38f91894
View on Chainz β†—

Difficulty

10.995449

Transactions

1

Size

201 B

Version

2

Bits

0afed5b8

Nonce

827,309,700

Timestamp

9/22/2019, 7:58:26 AM

Confirmations

3,468,588

Merkle Root

0c7dc57b3e4e727d0a2b9b77cc9132cd16d60baa061f129acee09cd9b876db2b
Transactions (1)
Coinbase0c7dc57b3e4e72…e09cd9b876db2b
1 in β†’ 1 out8.2600 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.

6.706 Γ— 10⁹⁢(97-digit number)
67066705933953081238…51496064876920422400
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
6.706 Γ— 10⁹⁢(97-digit number)
67066705933953081238…51496064876920422399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.341 Γ— 10⁹⁷(98-digit number)
13413341186790616247…02992129753840844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.682 Γ— 10⁹⁷(98-digit number)
26826682373581232495…05984259507681689599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.365 Γ— 10⁹⁷(98-digit number)
53653364747162464990…11968519015363379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.073 Γ— 10⁹⁸(99-digit number)
10730672949432492998…23937038030726758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.146 Γ— 10⁹⁸(99-digit number)
21461345898864985996…47874076061453516799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.292 Γ— 10⁹⁸(99-digit number)
42922691797729971992…95748152122907033599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.584 Γ— 10⁹⁸(99-digit number)
85845383595459943985…91496304245814067199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.716 Γ— 10⁹⁹(100-digit number)
17169076719091988797…82992608491628134399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.433 Γ— 10⁹⁹(100-digit number)
34338153438183977594…65985216983256268799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.867 Γ— 10⁹⁹(100-digit number)
68676306876367955188…31970433966512537599
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 3364739

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 f239b333eb80b4e10d8de6b75862ff3480f344b7c403c99318dc92ba38f91894

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 #3,364,739 on Chainz β†—
Circulating Supply:57,910,809 XPMΒ·at block #6,833,326 Β· updates every 60s
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