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Home/Chain Registry/Block #2,038,725

Block #2,038,725

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/26/2017, 1:38:17 AM Β· Difficulty 10.6808 Β· 4,805,306 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ef7c9930b14c5d0a7faebe06101adb34290ef7604929a580bb938b90a84bbaa7
View on Chainz β†—

Difficulty

10.680810

Transactions

1

Size

200 B

Version

2

Bits

0aae498e

Nonce

1,051,869,141

Timestamp

3/26/2017, 1:38:17 AM

Confirmations

4,805,306

Merkle Root

66c8a39eec83df30c83926fc8e57a26829cfc6774019de729eb2f47015ec8ea7
Transactions (1)
Coinbase66c8a39eec83df…b2f47015ec8ea7
1 in β†’ 1 out8.7500 XPM110 B
AcVpk4j6…LgmMK9s7
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.

8.800 Γ— 10⁹⁴(95-digit number)
88008858519760691201…47751554639448634880
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
8.800 Γ— 10⁹⁴(95-digit number)
88008858519760691201…47751554639448634881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.760 Γ— 10⁹⁡(96-digit number)
17601771703952138240…95503109278897269761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.520 Γ— 10⁹⁡(96-digit number)
35203543407904276480…91006218557794539521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.040 Γ— 10⁹⁡(96-digit number)
70407086815808552961…82012437115589079041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.408 Γ— 10⁹⁢(97-digit number)
14081417363161710592…64024874231178158081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.816 Γ— 10⁹⁢(97-digit number)
28162834726323421184…28049748462356316161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.632 Γ— 10⁹⁢(97-digit number)
56325669452646842368…56099496924712632321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.126 Γ— 10⁹⁷(98-digit number)
11265133890529368473…12198993849425264641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.253 Γ— 10⁹⁷(98-digit number)
22530267781058736947…24397987698850529281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.506 Γ— 10⁹⁷(98-digit number)
45060535562117473895…48795975397701058561
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 2038725

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 ef7c9930b14c5d0a7faebe06101adb34290ef7604929a580bb938b90a84bbaa7

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 #2,038,725 on Chainz β†—
Circulating Supply:57,996,625 XPMΒ·at block #6,844,030 Β· updates every 60s
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