XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #299,875

Block #299,875

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/8/2013, 6:15:04 AM Β· Difficulty 9.9922 Β· 6,496,991 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7dab8a65d42bfcf259717c40da4a540f9611ff628ab8b7f20ddfe334a97ceb00
View on Chainz β†—

Height

#299,875

Difficulty

9.992166

Transactions

1

Size

185 B

Version

2

Bits

09fdfe9d

Nonce

58,086

Timestamp

12/8/2013, 6:15:04 AM

Confirmations

6,496,991

Merkle Root

b1e1dfe377a022a60c2f6c0062c7e20ddb426febc56c8e268b955e56321bebf2
Transactions (1)
Coinbaseb1e1dfe377a022…955e56321bebf2
1 in β†’ 1 out10.0000 XPM97 B
Abopjr7Z…zLTB81mz
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.

5.250 Γ— 10⁹⁰(91-digit number)
52506667150929586602…89576486256357096320
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
5.250 Γ— 10⁹⁰(91-digit number)
52506667150929586602…89576486256357096321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.050 Γ— 10⁹¹(92-digit number)
10501333430185917320…79152972512714192641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.100 Γ— 10⁹¹(92-digit number)
21002666860371834640…58305945025428385281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.200 Γ— 10⁹¹(92-digit number)
42005333720743669281…16611890050856770561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.401 Γ— 10⁹¹(92-digit number)
84010667441487338563…33223780101713541121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.680 Γ— 10⁹²(93-digit number)
16802133488297467712…66447560203427082241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.360 Γ— 10⁹²(93-digit number)
33604266976594935425…32895120406854164481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.720 Γ— 10⁹²(93-digit number)
67208533953189870850…65790240813708328961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.344 Γ— 10⁹³(94-digit number)
13441706790637974170…31580481627416657921
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 299875

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 7dab8a65d42bfcf259717c40da4a540f9611ff628ab8b7f20ddfe334a97ceb00

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 #299,875 on Chainz β†—
Circulating Supply:57,618,943 XPMΒ·at block #6,796,865 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK