XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,171,667

Block #2,171,667

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/22/2017, 5:54:43 AM Β· Difficulty 10.9061 Β· 4,672,075 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1a9e889e0931c49ec74ce9b39af20ae101dade36e1d9094231bfa2c05d487f70
View on Chainz β†—

Difficulty

10.906085

Transactions

1

Size

200 B

Version

2

Bits

0ae7f538

Nonce

371,946,693

Timestamp

6/22/2017, 5:54:43 AM

Confirmations

4,672,075

Merkle Root

cec6f811f9ecd217a901b39c8a94263aedb40d366dd1a67a2f962b0061ad5daa
Transactions (1)
Coinbasecec6f811f9ecd2…962b0061ad5daa
1 in β†’ 1 out8.3900 XPM110 B
AJtykJzV…TrRe6huU
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.

8.061 Γ— 10⁹⁡(96-digit number)
80614928636191053938…16017133136060602880
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
8.061 Γ— 10⁹⁡(96-digit number)
80614928636191053938…16017133136060602879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁢(97-digit number)
16122985727238210787…32034266272121205759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.224 Γ— 10⁹⁢(97-digit number)
32245971454476421575…64068532544242411519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.449 Γ— 10⁹⁢(97-digit number)
64491942908952843150…28137065088484823039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.289 Γ— 10⁹⁷(98-digit number)
12898388581790568630…56274130176969646079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.579 Γ— 10⁹⁷(98-digit number)
25796777163581137260…12548260353939292159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.159 Γ— 10⁹⁷(98-digit number)
51593554327162274520…25096520707878584319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.031 Γ— 10⁹⁸(99-digit number)
10318710865432454904…50193041415757168639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.063 Γ— 10⁹⁸(99-digit number)
20637421730864909808…00386082831514337279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.127 Γ— 10⁹⁸(99-digit number)
41274843461729819616…00772165663028674559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.254 Γ— 10⁹⁸(99-digit number)
82549686923459639233…01544331326057349119
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 2171667

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 1a9e889e0931c49ec74ce9b39af20ae101dade36e1d9094231bfa2c05d487f70

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 #2,171,667 on Chainz β†—
Circulating Supply:57,994,305 XPMΒ·at block #6,843,741 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