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Home/Chain Registry/Block #2,738,152

Block #2,738,152

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/7/2018, 3:05:10 PM Β· Difficulty 11.6126 Β· 4,095,314 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
38098cc2e3530b3218fa97c3fefed6ce2dfad78b984759c7531c04a267435d33
View on Chainz β†—

Difficulty

11.612556

Transactions

1

Size

201 B

Version

2

Bits

0b9cd072

Nonce

27,690,255

Timestamp

7/7/2018, 3:05:10 PM

Confirmations

4,095,314

Merkle Root

4a020a3eb8c9b9f8f9ef77a034ab104f8e26d77d42bd3ddb04e0d700e50c8a99
Transactions (1)
Coinbase4a020a3eb8c9b9…e0d700e50c8a99
1 in β†’ 1 out7.4000 XPM110 B
AafWJuvE…X98XFAwn
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.

2.374 Γ— 10⁹⁷(98-digit number)
23749668030566942254…94337297371440814080
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
2.374 Γ— 10⁹⁷(98-digit number)
23749668030566942254…94337297371440814079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.749 Γ— 10⁹⁷(98-digit number)
47499336061133884509…88674594742881628159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.499 Γ— 10⁹⁷(98-digit number)
94998672122267769019…77349189485763256319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.899 Γ— 10⁹⁸(99-digit number)
18999734424453553803…54698378971526512639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.799 Γ— 10⁹⁸(99-digit number)
37999468848907107607…09396757943053025279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.599 Γ— 10⁹⁸(99-digit number)
75998937697814215215…18793515886106050559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.519 Γ— 10⁹⁹(100-digit number)
15199787539562843043…37587031772212101119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.039 Γ— 10⁹⁹(100-digit number)
30399575079125686086…75174063544424202239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.079 Γ— 10⁹⁹(100-digit number)
60799150158251372172…50348127088848404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.215 Γ— 10¹⁰⁰(101-digit number)
12159830031650274434…00696254177696808959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.431 Γ— 10¹⁰⁰(101-digit number)
24319660063300548869…01392508355393617919
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 2738152

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 38098cc2e3530b3218fa97c3fefed6ce2dfad78b984759c7531c04a267435d33

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 #2,738,152 on Chainz β†—
Circulating Supply:57,911,929 XPMΒ·at block #6,833,465 Β· updates every 60s
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