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Home/Chain Registry/Block #3,005,352

Block #3,005,352

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/11/2019, 7:19:33 PM Β· Difficulty 11.2004 Β· 3,836,893 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
39e78daa37a715eae5f120e033a17e96fddd3ce522d0fb68034a0f3c80759f72
View on Chainz β†—

Difficulty

11.200394

Transactions

1

Size

201 B

Version

2

Bits

0b334d0c

Nonce

1,496,726,319

Timestamp

1/11/2019, 7:19:33 PM

Confirmations

3,836,893

Merkle Root

209b0d354a697ef6431c91a43377bf2ac0bb7ab1cd54f1dd55faca01ca6dbb41
Transactions (1)
Coinbase209b0d354a697e…faca01ca6dbb41
1 in β†’ 1 out7.9600 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.788 Γ— 10⁹⁷(98-digit number)
37883486480503870674…81328315446134860800
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
3.788 Γ— 10⁹⁷(98-digit number)
37883486480503870674…81328315446134860799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.576 Γ— 10⁹⁷(98-digit number)
75766972961007741349…62656630892269721599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.515 Γ— 10⁹⁸(99-digit number)
15153394592201548269…25313261784539443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.030 Γ— 10⁹⁸(99-digit number)
30306789184403096539…50626523569078886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.061 Γ— 10⁹⁸(99-digit number)
60613578368806193079…01253047138157772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.212 Γ— 10⁹⁹(100-digit number)
12122715673761238615…02506094276315545599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.424 Γ— 10⁹⁹(100-digit number)
24245431347522477231…05012188552631091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.849 Γ— 10⁹⁹(100-digit number)
48490862695044954463…10024377105262182399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.698 Γ— 10⁹⁹(100-digit number)
96981725390089908926…20048754210524364799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.939 Γ— 10¹⁰⁰(101-digit number)
19396345078017981785…40097508421048729599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.879 Γ— 10¹⁰⁰(101-digit number)
38792690156035963570…80195016842097459199
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 3005352

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 39e78daa37a715eae5f120e033a17e96fddd3ce522d0fb68034a0f3c80759f72

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 #3,005,352 on Chainz β†—
Circulating Supply:57,982,358 XPMΒ·at block #6,842,244 Β· updates every 60s
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