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Home/Chain Registry/Block #3,086,964

Block #3,086,964

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/10/2019, 2:02:27 PM Β· Difficulty 11.0389 Β· 3,751,143 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8d917501e00a50c1cbd68dffa7e719da62984795ade2090d3ed2e0576f97b3ff
View on Chainz β†—

Difficulty

11.038937

Transactions

1

Size

199 B

Version

2

Bits

0b09f7bf

Nonce

1,042,322,002

Timestamp

3/10/2019, 2:02:27 PM

Confirmations

3,751,143

Merkle Root

5353e533a104aabadea909caaa04def597f1b8758e227b09e8bd54c7b379e0bc
Transactions (1)
Coinbase5353e533a104aa…bd54c7b379e0bc
1 in β†’ 1 out8.1900 XPM109 B
AbXwmGxD…4XXYP765
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.

3.887 Γ— 10⁹⁴(95-digit number)
38874440041334534767…80154579586097539360
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
3.887 Γ— 10⁹⁴(95-digit number)
38874440041334534767…80154579586097539361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.774 Γ— 10⁹⁴(95-digit number)
77748880082669069535…60309159172195078721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.554 Γ— 10⁹⁡(96-digit number)
15549776016533813907…20618318344390157441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.109 Γ— 10⁹⁡(96-digit number)
31099552033067627814…41236636688780314881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.219 Γ— 10⁹⁡(96-digit number)
62199104066135255628…82473273377560629761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.243 Γ— 10⁹⁢(97-digit number)
12439820813227051125…64946546755121259521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.487 Γ— 10⁹⁢(97-digit number)
24879641626454102251…29893093510242519041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.975 Γ— 10⁹⁢(97-digit number)
49759283252908204502…59786187020485038081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.951 Γ— 10⁹⁢(97-digit number)
99518566505816409005…19572374040970076161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.990 Γ— 10⁹⁷(98-digit number)
19903713301163281801…39144748081940152321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.980 Γ— 10⁹⁷(98-digit number)
39807426602326563602…78289496163880304641
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 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
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 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 3086964

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 8d917501e00a50c1cbd68dffa7e719da62984795ade2090d3ed2e0576f97b3ff

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 #3,086,964 on Chainz β†—
Circulating Supply:57,949,210 XPMΒ·at block #6,838,106 Β· updates every 60s
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