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Home/Chain Registry/Block #2,943,276

Block #2,943,276

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2018, 5:08:38 PM Β· Difficulty 11.3937 Β· 3,898,419 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5bd488d9c02e92a6997ca0a697944a0c835b3c1ec851ce6bc80c6ad2b3c158a3
View on Chainz β†—

Difficulty

11.393717

Transactions

1

Size

201 B

Version

2

Bits

0b64caa8

Nonce

1,713,419,162

Timestamp

11/28/2018, 5:08:38 PM

Confirmations

3,898,419

Merkle Root

2e894a34f78ecb6c07a7a62c0a8bcd360a38a345f3f0067e3ea1fb0f06da86f7
Transactions (1)
Coinbase2e894a34f78ecb…a1fb0f06da86f7
1 in β†’ 1 out7.6900 XPM110 B
AbXwmGxD…4XXYP765
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.

4.153 Γ— 10⁹⁢(97-digit number)
41532993794485323021…08966613477604720640
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
4.153 Γ— 10⁹⁢(97-digit number)
41532993794485323021…08966613477604720641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.306 Γ— 10⁹⁢(97-digit number)
83065987588970646042…17933226955209441281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.661 Γ— 10⁹⁷(98-digit number)
16613197517794129208…35866453910418882561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.322 Γ— 10⁹⁷(98-digit number)
33226395035588258416…71732907820837765121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.645 Γ— 10⁹⁷(98-digit number)
66452790071176516833…43465815641675530241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.329 Γ— 10⁹⁸(99-digit number)
13290558014235303366…86931631283351060481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.658 Γ— 10⁹⁸(99-digit number)
26581116028470606733…73863262566702120961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.316 Γ— 10⁹⁸(99-digit number)
53162232056941213467…47726525133404241921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.063 Γ— 10⁹⁹(100-digit number)
10632446411388242693…95453050266808483841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.126 Γ— 10⁹⁹(100-digit number)
21264892822776485386…90906100533616967681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.252 Γ— 10⁹⁹(100-digit number)
42529785645552970773…81812201067233935361
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 2943276

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 5bd488d9c02e92a6997ca0a697944a0c835b3c1ec851ce6bc80c6ad2b3c158a3

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 #2,943,276 on Chainz β†—
Circulating Supply:57,977,938 XPMΒ·at block #6,841,694 Β· updates every 60s
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