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Home/Chain Registry/Block #3,053,876

Block #3,053,876

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/15/2019, 12:06:52 PM Β· Difficulty 10.9961 Β· 3,786,808 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9825860932aab57a3a5066bd2035b3ef354f7dc0acf98c233949df075ecd26ab
View on Chainz β†—

Difficulty

10.996091

Transactions

2

Size

3.74 KB

Version

2

Bits

0afeffcc

Nonce

120,192,425

Timestamp

2/15/2019, 12:06:52 PM

Confirmations

3,786,808

Merkle Root

6471f09c5228eedffb93a04890dba7b8e758cb314f649372d4c801393600e685
Transactions (2)
Coinbase006779a04fe5aa…40e8a56776fb03
1 in β†’ 1 out8.3100 XPM110 B
AUhjokok…k5m93PZR
e90106b9325cc0…b7ecca42a363ca
24 in β†’ 2 out5000.0100 XPM3.54 KB
AUWLiCGG…uTwceacQANrr2f3X…a7jBiq7s
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.

6.589 Γ— 10⁹⁴(95-digit number)
65897127170021701225…29521269385895030320
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
6.589 Γ— 10⁹⁴(95-digit number)
65897127170021701225…29521269385895030321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.317 Γ— 10⁹⁡(96-digit number)
13179425434004340245…59042538771790060641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.635 Γ— 10⁹⁡(96-digit number)
26358850868008680490…18085077543580121281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.271 Γ— 10⁹⁡(96-digit number)
52717701736017360980…36170155087160242561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.054 Γ— 10⁹⁢(97-digit number)
10543540347203472196…72340310174320485121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.108 Γ— 10⁹⁢(97-digit number)
21087080694406944392…44680620348640970241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.217 Γ— 10⁹⁢(97-digit number)
42174161388813888784…89361240697281940481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.434 Γ— 10⁹⁢(97-digit number)
84348322777627777568…78722481394563880961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.686 Γ— 10⁹⁷(98-digit number)
16869664555525555513…57444962789127761921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.373 Γ— 10⁹⁷(98-digit number)
33739329111051111027…14889925578255523841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.747 Γ— 10⁹⁷(98-digit number)
67478658222102222054…29779851156511047681
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 3053876

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 9825860932aab57a3a5066bd2035b3ef354f7dc0acf98c233949df075ecd26ab

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 #3,053,876 on Chainz β†—
Circulating Supply:57,969,810 XPMΒ·at block #6,840,683 Β· updates every 60s
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