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Home/Chain Registry/Block #2,855,607

Block #2,855,607

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/26/2018, 8:48:49 AM Β· Difficulty 11.6980 Β· 3,977,547 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
63a0afb68c80e69042495a66383235a872250d183cf47798d8031a8d19de3e1a
View on Chainz β†—

Difficulty

11.698049

Transactions

1

Size

200 B

Version

2

Bits

0bb2b35c

Nonce

1,483,545,700

Timestamp

9/26/2018, 8:48:49 AM

Confirmations

3,977,547

Merkle Root

bd043949142572a4e8f98d88863d29396104d0aceac3a3a1e2e6e8495f530dab
Transactions (1)
Coinbasebd043949142572…e6e8495f530dab
1 in β†’ 1 out7.3000 XPM109 B
ALQGpaT6…9dLVU1B9
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.

4.206 Γ— 10⁹⁢(97-digit number)
42061737818960347640…73397246242099240960
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
4.206 Γ— 10⁹⁢(97-digit number)
42061737818960347640…73397246242099240959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.412 Γ— 10⁹⁢(97-digit number)
84123475637920695280…46794492484198481919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.682 Γ— 10⁹⁷(98-digit number)
16824695127584139056…93588984968396963839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.364 Γ— 10⁹⁷(98-digit number)
33649390255168278112…87177969936793927679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.729 Γ— 10⁹⁷(98-digit number)
67298780510336556224…74355939873587855359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.345 Γ— 10⁹⁸(99-digit number)
13459756102067311244…48711879747175710719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.691 Γ— 10⁹⁸(99-digit number)
26919512204134622489…97423759494351421439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.383 Γ— 10⁹⁸(99-digit number)
53839024408269244979…94847518988702842879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.076 Γ— 10⁹⁹(100-digit number)
10767804881653848995…89695037977405685759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.153 Γ— 10⁹⁹(100-digit number)
21535609763307697991…79390075954811371519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.307 Γ— 10⁹⁹(100-digit number)
43071219526615395983…58780151909622743039
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 2855607

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 63a0afb68c80e69042495a66383235a872250d183cf47798d8031a8d19de3e1a

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 #2,855,607 on Chainz β†—
Circulating Supply:57,909,410 XPMΒ·at block #6,833,153 Β· updates every 60s
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