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Home/Chain Registry/Block #3,010,105

Block #3,010,105

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/15/2019, 2:31:44 AM Β· Difficulty 11.2006 Β· 3,828,950 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2905c8494c039815e946123937d2e33635ef06c55b9c1678e6ba3376643492f8
View on Chainz β†—

Difficulty

11.200584

Transactions

1

Size

201 B

Version

2

Bits

0b335974

Nonce

361,315,306

Timestamp

1/15/2019, 2:31:44 AM

Confirmations

3,828,950

Merkle Root

f6028c9ddb82a3734724b4be8c3e6fdd144cc3e1826b8eb59a8f3dfbb313eef0
Transactions (1)
Coinbasef6028c9ddb82a3…8f3dfbb313eef0
1 in β†’ 1 out7.9600 XPM110 B
AUhjokok…k5m93PZR
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.

4.708 Γ— 10⁹⁢(97-digit number)
47087194817778435192…05951368700061582080
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
4.708 Γ— 10⁹⁢(97-digit number)
47087194817778435192…05951368700061582079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.417 Γ— 10⁹⁢(97-digit number)
94174389635556870384…11902737400123164159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.883 Γ— 10⁹⁷(98-digit number)
18834877927111374076…23805474800246328319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.766 Γ— 10⁹⁷(98-digit number)
37669755854222748153…47610949600492656639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.533 Γ— 10⁹⁷(98-digit number)
75339511708445496307…95221899200985313279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.506 Γ— 10⁹⁸(99-digit number)
15067902341689099261…90443798401970626559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.013 Γ— 10⁹⁸(99-digit number)
30135804683378198523…80887596803941253119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.027 Γ— 10⁹⁸(99-digit number)
60271609366756397046…61775193607882506239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.205 Γ— 10⁹⁹(100-digit number)
12054321873351279409…23550387215765012479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.410 Γ— 10⁹⁹(100-digit number)
24108643746702558818…47100774431530024959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.821 Γ— 10⁹⁹(100-digit number)
48217287493405117636…94201548863060049919
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 3010105

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 2905c8494c039815e946123937d2e33635ef06c55b9c1678e6ba3376643492f8

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 #3,010,105 on Chainz β†—
Circulating Supply:57,956,707 XPMΒ·at block #6,839,054 Β· updates every 60s
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