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Home/Chain Registry/Block #2,786,787

Block #2,786,787

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2018, 7:52:09 PM Β· Difficulty 11.6729 Β· 4,050,157 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ec60e1fb8aa4bd6cc428f829541abc62102faaefe82d6dd18f9e5bbce6d95dd5
View on Chainz β†—

Difficulty

11.672888

Transactions

1

Size

200 B

Version

2

Bits

0bac4263

Nonce

1,497,496,156

Timestamp

8/9/2018, 7:52:09 PM

Confirmations

4,050,157

Merkle Root

601e4ef3611e73e1253ab792b8db4d194663b5d8ec877bc0bb9f4dc3bec85ea8
Transactions (1)
Coinbase601e4ef3611e73…9f4dc3bec85ea8
1 in β†’ 1 out7.3300 XPM109 B
AJbsQjyd…Fj1XSwkt
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.

7.823 Γ— 10⁹⁡(96-digit number)
78237442563517903482…36359214700316043520
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
7.823 Γ— 10⁹⁡(96-digit number)
78237442563517903482…36359214700316043521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.564 Γ— 10⁹⁢(97-digit number)
15647488512703580696…72718429400632087041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.129 Γ— 10⁹⁢(97-digit number)
31294977025407161392…45436858801264174081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.258 Γ— 10⁹⁢(97-digit number)
62589954050814322785…90873717602528348161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.251 Γ— 10⁹⁷(98-digit number)
12517990810162864557…81747435205056696321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.503 Γ— 10⁹⁷(98-digit number)
25035981620325729114…63494870410113392641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.007 Γ— 10⁹⁷(98-digit number)
50071963240651458228…26989740820226785281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.001 Γ— 10⁹⁸(99-digit number)
10014392648130291645…53979481640453570561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.002 Γ— 10⁹⁸(99-digit number)
20028785296260583291…07958963280907141121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.005 Γ— 10⁹⁸(99-digit number)
40057570592521166583…15917926561814282241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.011 Γ— 10⁹⁸(99-digit number)
80115141185042333166…31835853123628564481
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 2786787

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 ec60e1fb8aa4bd6cc428f829541abc62102faaefe82d6dd18f9e5bbce6d95dd5

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 #2,786,787 on Chainz β†—
Circulating Supply:57,939,850 XPMΒ·at block #6,836,943 Β· updates every 60s
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