XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,644,216

Block #2,644,216

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 9:51:50 AM Β· Difficulty 11.7046 Β· 4,201,122 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e6e61e6218bddfcb5f879d90466077744ded7e7550a76134eed38e9b71aa50b
View on Chainz β†—

Difficulty

11.704632

Transactions

1

Size

200 B

Version

2

Bits

0bb462cb

Nonce

1,714,145,574

Timestamp

5/2/2018, 9:51:50 AM

Confirmations

4,201,122

Merkle Root

db1bad8ff5483b34177aae4d06aca8a19c6760ecef8728b323a7c7e3a64bb22b
Transactions (1)
Coinbasedb1bad8ff5483b…a7c7e3a64bb22b
1 in β†’ 1 out7.2900 XPM110 B
ASBDQ7zs…z3i2hb6h
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.

1.364 Γ— 10⁹⁡(96-digit number)
13648286901781995118…48422015903315059390
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
1.364 Γ— 10⁹⁡(96-digit number)
13648286901781995118…48422015903315059389
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.729 Γ— 10⁹⁡(96-digit number)
27296573803563990237…96844031806630118779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.459 Γ— 10⁹⁡(96-digit number)
54593147607127980475…93688063613260237559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.091 Γ— 10⁹⁢(97-digit number)
10918629521425596095…87376127226520475119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.183 Γ— 10⁹⁢(97-digit number)
21837259042851192190…74752254453040950239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.367 Γ— 10⁹⁢(97-digit number)
43674518085702384380…49504508906081900479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.734 Γ— 10⁹⁢(97-digit number)
87349036171404768760…99009017812163800959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.746 Γ— 10⁹⁷(98-digit number)
17469807234280953752…98018035624327601919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.493 Γ— 10⁹⁷(98-digit number)
34939614468561907504…96036071248655203839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.987 Γ— 10⁹⁷(98-digit number)
69879228937123815008…92072142497310407679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.397 Γ— 10⁹⁸(99-digit number)
13975845787424763001…84144284994620815359
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 2644216

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 4e6e61e6218bddfcb5f879d90466077744ded7e7550a76134eed38e9b71aa50b

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 #2,644,216 on Chainz β†—
Circulating Supply:58,007,146 XPMΒ·at block #6,845,337 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