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Home/Chain Registry/Block #2,693,643

Block #2,693,643

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/6/2018, 1:24:59 AM Β· Difficulty 11.6778 Β· 4,146,613 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
30d0373df5ee57c35865130ead9695493e3ff75cdb0c5a7a744e773142d2cc22
View on Chainz β†—

Difficulty

11.677832

Transactions

1

Size

200 B

Version

2

Bits

0bad8669

Nonce

82,953,995

Timestamp

6/6/2018, 1:24:59 AM

Confirmations

4,146,613

Merkle Root

bc84d99f557e00ab4bee6d51f44cd4819779409bb7d7db462399eb4361c0dd07
Transactions (1)
Coinbasebc84d99f557e00…99eb4361c0dd07
1 in β†’ 1 out7.3200 XPM110 B
AMqn4axo…RZ5ojsRh
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.

5.413 Γ— 10⁹⁴(95-digit number)
54130619697834382548…29477512319648503650
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
5.413 Γ— 10⁹⁴(95-digit number)
54130619697834382548…29477512319648503651
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.082 Γ— 10⁹⁡(96-digit number)
10826123939566876509…58955024639297007301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.165 Γ— 10⁹⁡(96-digit number)
21652247879133753019…17910049278594014601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.330 Γ— 10⁹⁡(96-digit number)
43304495758267506038…35820098557188029201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.660 Γ— 10⁹⁡(96-digit number)
86608991516535012076…71640197114376058401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.732 Γ— 10⁹⁢(97-digit number)
17321798303307002415…43280394228752116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.464 Γ— 10⁹⁢(97-digit number)
34643596606614004830…86560788457504233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.928 Γ— 10⁹⁢(97-digit number)
69287193213228009661…73121576915008467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.385 Γ— 10⁹⁷(98-digit number)
13857438642645601932…46243153830016934401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.771 Γ— 10⁹⁷(98-digit number)
27714877285291203864…92486307660033868801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.542 Γ— 10⁹⁷(98-digit number)
55429754570582407729…84972615320067737601
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 2693643

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 30d0373df5ee57c35865130ead9695493e3ff75cdb0c5a7a744e773142d2cc22

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 #2,693,643 on Chainz β†—
Circulating Supply:57,966,363 XPMΒ·at block #6,840,255 Β· updates every 60s
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