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Home/Chain Registry/Block #2,169,418

Block #2,169,418

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/20/2017, 9:54:32 PM Β· Difficulty 10.8997 Β· 4,671,381 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
71f9cd7c56b0f2b14d4cd767c28e28f05ae04e449ed136ab8b6a5198503b706d
View on Chainz β†—

Difficulty

10.899689

Transactions

1

Size

199 B

Version

2

Bits

0ae65208

Nonce

1,152,901,888

Timestamp

6/20/2017, 9:54:32 PM

Confirmations

4,671,381

Merkle Root

3ebb82d841053adb377787f21af06203bb72a06d5f2067d864fec0b2a83e9fc0
Transactions (1)
Coinbase3ebb82d841053a…fec0b2a83e9fc0
1 in β†’ 1 out8.4000 XPM109 B
AS49mSPT…GTida9ie
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.

9.703 Γ— 10⁹⁴(95-digit number)
97037275096780791806…29002831111981495680
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
9.703 Γ— 10⁹⁴(95-digit number)
97037275096780791806…29002831111981495681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.940 Γ— 10⁹⁡(96-digit number)
19407455019356158361…58005662223962991361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.881 Γ— 10⁹⁡(96-digit number)
38814910038712316722…16011324447925982721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.762 Γ— 10⁹⁡(96-digit number)
77629820077424633445…32022648895851965441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.552 Γ— 10⁹⁢(97-digit number)
15525964015484926689…64045297791703930881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.105 Γ— 10⁹⁢(97-digit number)
31051928030969853378…28090595583407861761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.210 Γ— 10⁹⁢(97-digit number)
62103856061939706756…56181191166815723521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.242 Γ— 10⁹⁷(98-digit number)
12420771212387941351…12362382333631447041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.484 Γ— 10⁹⁷(98-digit number)
24841542424775882702…24724764667262894081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.968 Γ— 10⁹⁷(98-digit number)
49683084849551765405…49449529334525788161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2169418

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 71f9cd7c56b0f2b14d4cd767c28e28f05ae04e449ed136ab8b6a5198503b706d

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 #2,169,418 on Chainz β†—
Circulating Supply:57,970,740 XPMΒ·at block #6,840,798 Β· updates every 60s
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