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Home/Chain Registry/Block #2,497,381

Block #2,497,381

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/30/2018, 10:28:38 AM Β· Difficulty 10.9746 Β· 4,343,574 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f941099a2ee33d1473cd000cfe7e5d8c138989ccc6390acde6fd8f146f1a5420
View on Chainz β†—

Difficulty

10.974628

Transactions

1

Size

243 B

Version

2

Bits

0af9813d

Nonce

2,503,433,887

Timestamp

1/30/2018, 10:28:38 AM

Confirmations

4,343,574

Merkle Root

37f9e67481b3cff12c6d8b73d14f42acb802539d60baa66137a207e97d316e27
Transactions (1)
Coinbase37f9e67481b3cf…a207e97d316e27
1 in β†’ 2 out8.2900 XPM152 B
ARvAvVHT…tKqRnMrLAXbk7f7A…Tx7JECPG
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.

1.009 Γ— 10⁹⁢(97-digit number)
10097488836678397712…56129586103124380360
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
1.009 Γ— 10⁹⁢(97-digit number)
10097488836678397712…56129586103124380361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.019 Γ— 10⁹⁢(97-digit number)
20194977673356795425…12259172206248760721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.038 Γ— 10⁹⁢(97-digit number)
40389955346713590851…24518344412497521441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.077 Γ— 10⁹⁢(97-digit number)
80779910693427181703…49036688824995042881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.615 Γ— 10⁹⁷(98-digit number)
16155982138685436340…98073377649990085761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.231 Γ— 10⁹⁷(98-digit number)
32311964277370872681…96146755299980171521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.462 Γ— 10⁹⁷(98-digit number)
64623928554741745362…92293510599960343041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.292 Γ— 10⁹⁸(99-digit number)
12924785710948349072…84587021199920686081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.584 Γ— 10⁹⁸(99-digit number)
25849571421896698145…69174042399841372161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.169 Γ— 10⁹⁸(99-digit number)
51699142843793396290…38348084799682744321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.033 Γ— 10⁹⁹(100-digit number)
10339828568758679258…76696169599365488641
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 2497381

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 f941099a2ee33d1473cd000cfe7e5d8c138989ccc6390acde6fd8f146f1a5420

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 #2,497,381 on Chainz β†—
Circulating Supply:57,971,995 XPMΒ·at block #6,840,954 Β· updates every 60s
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