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Home/Chain Registry/Block #2,840,451

Block #2,840,451

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/15/2018, 1:43:12 PM Β· Difficulty 11.7200 Β· 3,997,685 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
969f95b736532b5f341b222629dd04ae86489fb886b21f140db42f469624581d
View on Chainz β†—

Difficulty

11.719963

Transactions

1

Size

200 B

Version

2

Bits

0bb84f78

Nonce

1,026,695,678

Timestamp

9/15/2018, 1:43:12 PM

Confirmations

3,997,685

Merkle Root

bbb039d86de05a545747af3af0f0f9f12abec01f0018f53c0b4b3938d76ef2e5
Transactions (1)
Coinbasebbb039d86de05a…4b3938d76ef2e5
1 in β†’ 1 out7.2700 XPM110 B
AbjsXQ6D…Kdmzwcxr
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.

1.905 Γ— 10⁹⁡(96-digit number)
19055498662984791547…09769148432392611760
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
1.905 Γ— 10⁹⁡(96-digit number)
19055498662984791547…09769148432392611761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.811 Γ— 10⁹⁡(96-digit number)
38110997325969583094…19538296864785223521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.622 Γ— 10⁹⁡(96-digit number)
76221994651939166189…39076593729570447041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.524 Γ— 10⁹⁢(97-digit number)
15244398930387833237…78153187459140894081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.048 Γ— 10⁹⁢(97-digit number)
30488797860775666475…56306374918281788161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.097 Γ— 10⁹⁢(97-digit number)
60977595721551332951…12612749836563576321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.219 Γ— 10⁹⁷(98-digit number)
12195519144310266590…25225499673127152641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.439 Γ— 10⁹⁷(98-digit number)
24391038288620533180…50450999346254305281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.878 Γ— 10⁹⁷(98-digit number)
48782076577241066361…00901998692508610561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.756 Γ— 10⁹⁷(98-digit number)
97564153154482132723…01803997385017221121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.951 Γ— 10⁹⁸(99-digit number)
19512830630896426544…03607994770034442241
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 2840451

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 969f95b736532b5f341b222629dd04ae86489fb886b21f140db42f469624581d

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 #2,840,451 on Chainz β†—
Circulating Supply:57,949,356 XPMΒ·at block #6,838,135 Β· updates every 60s
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