XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,717,389

Block #2,717,389

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 6/23/2018, 4:03:37 AM Β· Difficulty 11.6164 Β· 4,122,397 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1a726c7b3e4f4a3ab0cba9c7fa10deeed2163f3477f910e38906bc38be21ddac
View on Chainz β†—

Difficulty

11.616377

Transactions

1

Size

200 B

Version

2

Bits

0b9dcadd

Nonce

395,923,004

Timestamp

6/23/2018, 4:03:37 AM

Confirmations

4,122,397

Merkle Root

f4e67ec36fbfb95b1e2988dec88187ca5dfa84a191d4ea4a5b84e45a1e476e81
Transactions (1)
Coinbasef4e67ec36fbfb9…84e45a1e476e81
1 in β†’ 1 out7.4000 XPM110 B
AZtxQr2F…7grUWrUz
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.

3.945 Γ— 10⁹⁡(96-digit number)
39450039801889387301…66063152305440868800
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
3.945 Γ— 10⁹⁡(96-digit number)
39450039801889387301…66063152305440868799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.890 Γ— 10⁹⁡(96-digit number)
78900079603778774602…32126304610881737599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.578 Γ— 10⁹⁢(97-digit number)
15780015920755754920…64252609221763475199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.156 Γ— 10⁹⁢(97-digit number)
31560031841511509840…28505218443526950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.312 Γ— 10⁹⁢(97-digit number)
63120063683023019681…57010436887053900799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.262 Γ— 10⁹⁷(98-digit number)
12624012736604603936…14020873774107801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.524 Γ— 10⁹⁷(98-digit number)
25248025473209207872…28041747548215603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.049 Γ— 10⁹⁷(98-digit number)
50496050946418415745…56083495096431206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.009 Γ— 10⁹⁸(99-digit number)
10099210189283683149…12166990192862412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.019 Γ— 10⁹⁸(99-digit number)
20198420378567366298…24333980385724825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.039 Γ— 10⁹⁸(99-digit number)
40396840757134732596…48667960771449651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
8.079 Γ— 10⁹⁸(99-digit number)
80793681514269465192…97335921542899302399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2717389

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 1a726c7b3e4f4a3ab0cba9c7fa10deeed2163f3477f910e38906bc38be21ddac

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 #2,717,389 on Chainz β†—
Circulating Supply:57,962,579 XPMΒ·at block #6,839,785 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