XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,685,400

Block #2,685,400

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2018, 5:22:07 AM Β· Difficulty 11.6876 Β· 4,157,011 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8c3a6b5f1cc3fc3eae2660e0fe0cd3d24d43e29054d23f45e3190189ed66fd7e
View on Chainz β†—

Difficulty

11.687611

Transactions

1

Size

201 B

Version

2

Bits

0bb00749

Nonce

323,379,661

Timestamp

5/31/2018, 5:22:07 AM

Confirmations

4,157,011

Merkle Root

3eee39e11f3dbbf9a7d972666f30409898de7efc0a55bd58e54e7362d5b84ec7
Transactions (1)
Coinbase3eee39e11f3dbb…4e7362d5b84ec7
1 in β†’ 1 out7.3100 XPM110 B
Ac17kp2c…porfywoN
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.

1.045 Γ— 10⁹⁷(98-digit number)
10451286732679984857…74242075675850091520
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.045 Γ— 10⁹⁷(98-digit number)
10451286732679984857…74242075675850091519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.090 Γ— 10⁹⁷(98-digit number)
20902573465359969715…48484151351700183039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.180 Γ— 10⁹⁷(98-digit number)
41805146930719939430…96968302703400366079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.361 Γ— 10⁹⁷(98-digit number)
83610293861439878860…93936605406800732159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.672 Γ— 10⁹⁸(99-digit number)
16722058772287975772…87873210813601464319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.344 Γ— 10⁹⁸(99-digit number)
33444117544575951544…75746421627202928639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.688 Γ— 10⁹⁸(99-digit number)
66888235089151903088…51492843254405857279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.337 Γ— 10⁹⁹(100-digit number)
13377647017830380617…02985686508811714559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.675 Γ— 10⁹⁹(100-digit number)
26755294035660761235…05971373017623429119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.351 Γ— 10⁹⁹(100-digit number)
53510588071321522470…11942746035246858239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.070 Γ— 10¹⁰⁰(101-digit number)
10702117614264304494…23885492070493716479
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2685400

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 8c3a6b5f1cc3fc3eae2660e0fe0cd3d24d43e29054d23f45e3190189ed66fd7e

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 #2,685,400 on Chainz β†—
Circulating Supply:57,983,700 XPMΒ·at block #6,842,410 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.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy