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Home/Chain Registry/Block #2,788,682

Block #2,788,682

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/11/2018, 3:23:48 AM Β· Difficulty 11.6732 Β· 4,052,403 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2fa494dafeef4838e69ade976eac36aac5e86a8c7899a36f3e317b8ad312dfc3
View on Chainz β†—

Difficulty

11.673153

Transactions

1

Size

200 B

Version

2

Bits

0bac53c5

Nonce

1,157,440,450

Timestamp

8/11/2018, 3:23:48 AM

Confirmations

4,052,403

Merkle Root

c5c69d76a1cf9936e53c8135efc26f6aa562efd028e06541aa4b50feb280ec3a
Transactions (1)
Coinbasec5c69d76a1cf99…4b50feb280ec3a
1 in β†’ 1 out7.3300 XPM109 B
ATixWvSe…AQPqRhoc
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.

1.417 Γ— 10⁹⁸(99-digit number)
14173860715359318605…45115522708426014720
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
1.417 Γ— 10⁹⁸(99-digit number)
14173860715359318605…45115522708426014719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.834 Γ— 10⁹⁸(99-digit number)
28347721430718637210…90231045416852029439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.669 Γ— 10⁹⁸(99-digit number)
56695442861437274421…80462090833704058879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.133 Γ— 10⁹⁹(100-digit number)
11339088572287454884…60924181667408117759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.267 Γ— 10⁹⁹(100-digit number)
22678177144574909768…21848363334816235519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.535 Γ— 10⁹⁹(100-digit number)
45356354289149819537…43696726669632471039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.071 Γ— 10⁹⁹(100-digit number)
90712708578299639075…87393453339264942079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.814 Γ— 10¹⁰⁰(101-digit number)
18142541715659927815…74786906678529884159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.628 Γ— 10¹⁰⁰(101-digit number)
36285083431319855630…49573813357059768319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.257 Γ— 10¹⁰⁰(101-digit number)
72570166862639711260…99147626714119536639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.451 Γ— 10¹⁰¹(102-digit number)
14514033372527942252…98295253428239073279
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 2788682

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 2fa494dafeef4838e69ade976eac36aac5e86a8c7899a36f3e317b8ad312dfc3

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 #2,788,682 on Chainz β†—
Circulating Supply:57,973,043 XPMΒ·at block #6,841,084 Β· updates every 60s
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