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Home/Chain Registry/Block #2,857,060

Block #2,857,060

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/27/2018, 11:30:47 AM Β· Difficulty 11.6890 Β· 3,984,259 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e8ca7d8aed3de1f2a602fe353adca332174f30e434ef2cc8c490662d1e465c07
View on Chainz β†—

Difficulty

11.689003

Transactions

1

Size

200 B

Version

2

Bits

0bb0627c

Nonce

1,788,232,371

Timestamp

9/27/2018, 11:30:47 AM

Confirmations

3,984,259

Merkle Root

b3ccb5c19e181ddf8db118347b22f8c27245a7dbe66f90119d6f503d28bc72ea
Transactions (1)
Coinbaseb3ccb5c19e181d…6f503d28bc72ea
1 in β†’ 1 out7.3100 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.

1.999 Γ— 10⁹⁷(98-digit number)
19999646355225124809…49823222805257543680
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
1.999 Γ— 10⁹⁷(98-digit number)
19999646355225124809…49823222805257543681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.999 Γ— 10⁹⁷(98-digit number)
39999292710450249618…99646445610515087361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.999 Γ— 10⁹⁷(98-digit number)
79998585420900499237…99292891221030174721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.599 Γ— 10⁹⁸(99-digit number)
15999717084180099847…98585782442060349441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.199 Γ— 10⁹⁸(99-digit number)
31999434168360199695…97171564884120698881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.399 Γ— 10⁹⁸(99-digit number)
63998868336720399390…94343129768241397761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.279 Γ— 10⁹⁹(100-digit number)
12799773667344079878…88686259536482795521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.559 Γ— 10⁹⁹(100-digit number)
25599547334688159756…77372519072965591041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.119 Γ— 10⁹⁹(100-digit number)
51199094669376319512…54745038145931182081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.023 Γ— 10¹⁰⁰(101-digit number)
10239818933875263902…09490076291862364161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.047 Γ— 10¹⁰⁰(101-digit number)
20479637867750527804…18980152583724728321
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 2857060

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 e8ca7d8aed3de1f2a602fe353adca332174f30e434ef2cc8c490662d1e465c07

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 #2,857,060 on Chainz β†—
Circulating Supply:57,974,915 XPMΒ·at block #6,841,318 Β· updates every 60s
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