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Home/Chain Registry/Block #2,938,522

Block #2,938,522

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/25/2018, 12:15:42 PM Β· Difficulty 11.3767 Β· 3,906,404 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
377128222bf3fb723697ddfd652549f11ce6b0b552e5f3536d9268b492909d20
View on Chainz β†—

Difficulty

11.376667

Transactions

1

Size

201 B

Version

2

Bits

0b606d3a

Nonce

821,712,665

Timestamp

11/25/2018, 12:15:42 PM

Confirmations

3,906,404

Merkle Root

a47ee526036b3d5582eeb7434deb15a70104eb63e084595934cb19a0f2e5f680
Transactions (1)
Coinbasea47ee526036b3d…cb19a0f2e5f680
1 in β†’ 1 out7.7100 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.

4.325 Γ— 10⁹⁢(97-digit number)
43258998523994146740…12745401640290652160
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
4.325 Γ— 10⁹⁢(97-digit number)
43258998523994146740…12745401640290652161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.651 Γ— 10⁹⁢(97-digit number)
86517997047988293481…25490803280581304321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.730 Γ— 10⁹⁷(98-digit number)
17303599409597658696…50981606561162608641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.460 Γ— 10⁹⁷(98-digit number)
34607198819195317392…01963213122325217281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.921 Γ— 10⁹⁷(98-digit number)
69214397638390634784…03926426244650434561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.384 Γ— 10⁹⁸(99-digit number)
13842879527678126956…07852852489300869121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.768 Γ— 10⁹⁸(99-digit number)
27685759055356253913…15705704978601738241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.537 Γ— 10⁹⁸(99-digit number)
55371518110712507827…31411409957203476481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.107 Γ— 10⁹⁹(100-digit number)
11074303622142501565…62822819914406952961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.214 Γ— 10⁹⁹(100-digit number)
22148607244285003131…25645639828813905921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.429 Γ— 10⁹⁹(100-digit number)
44297214488570006262…51291279657627811841
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 2938522

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 377128222bf3fb723697ddfd652549f11ce6b0b552e5f3536d9268b492909d20

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 #2,938,522 on Chainz β†—
Circulating Supply:58,003,824 XPMΒ·at block #6,844,925 Β· updates every 60s
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