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Home/Chain Registry/Block #2,655,078

Block #2,655,078

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2018, 9:24:14 PM Β· Difficulty 11.7103 Β· 4,183,463 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c534778576e98005000fecd21aa0e6cbd6628f02bd5aeae13efef7733220c3d
View on Chainz β†—

Difficulty

11.710291

Transactions

1

Size

200 B

Version

2

Bits

0bb5d59c

Nonce

393,205,548

Timestamp

5/9/2018, 9:24:14 PM

Confirmations

4,183,463

Merkle Root

a1fee229feeec742e9186791406f306ac7549f3c58c03d758513e94301fc4ca8
Transactions (1)
Coinbasea1fee229feeec7…13e94301fc4ca8
1 in β†’ 1 out7.2800 XPM110 B
Adqah8zh…1WwoHJ9t
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.

3.941 Γ— 10⁹⁡(96-digit number)
39419607611060033128…07401914524560480000
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
3.941 Γ— 10⁹⁡(96-digit number)
39419607611060033128…07401914524560480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.883 Γ— 10⁹⁡(96-digit number)
78839215222120066256…14803829049120960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.576 Γ— 10⁹⁢(97-digit number)
15767843044424013251…29607658098241920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.153 Γ— 10⁹⁢(97-digit number)
31535686088848026502…59215316196483840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.307 Γ— 10⁹⁢(97-digit number)
63071372177696053005…18430632392967680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.261 Γ— 10⁹⁷(98-digit number)
12614274435539210601…36861264785935360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.522 Γ— 10⁹⁷(98-digit number)
25228548871078421202…73722529571870720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.045 Γ— 10⁹⁷(98-digit number)
50457097742156842404…47445059143741440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.009 Γ— 10⁹⁸(99-digit number)
10091419548431368480…94890118287482880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.018 Γ— 10⁹⁸(99-digit number)
20182839096862736961…89780236574965760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.036 Γ— 10⁹⁸(99-digit number)
40365678193725473923…79560473149931520001
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 2655078

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 7c534778576e98005000fecd21aa0e6cbd6628f02bd5aeae13efef7733220c3d

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 #2,655,078 on Chainz β†—
Circulating Supply:57,952,609 XPMΒ·at block #6,838,540 Β· updates every 60s
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