XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,451,567

Block #2,451,567

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/31/2017, 9:03:48 PM Β· Difficulty 10.9498 Β· 4,394,089 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab3f64d86946590653eb8542963ef47e9d3b12511fcd9227d6b42f8838318198
View on Chainz β†—

Difficulty

10.949756

Transactions

1

Size

201 B

Version

2

Bits

0af32336

Nonce

9,951,075

Timestamp

12/31/2017, 9:03:48 PM

Confirmations

4,394,089

Merkle Root

388d1f8ff28c35d3618479111d4332c53041a2d3696b42593144246d84aba15d
Transactions (1)
Coinbase388d1f8ff28c35…44246d84aba15d
1 in β†’ 1 out8.3300 XPM110 B
ARf6shku…9A6AbNee
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.

6.664 Γ— 10⁹⁢(97-digit number)
66646024404549827423…08719421187535636480
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
6.664 Γ— 10⁹⁢(97-digit number)
66646024404549827423…08719421187535636479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.332 Γ— 10⁹⁷(98-digit number)
13329204880909965484…17438842375071272959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.665 Γ— 10⁹⁷(98-digit number)
26658409761819930969…34877684750142545919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.331 Γ— 10⁹⁷(98-digit number)
53316819523639861939…69755369500285091839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.066 Γ— 10⁹⁸(99-digit number)
10663363904727972387…39510739000570183679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.132 Γ— 10⁹⁸(99-digit number)
21326727809455944775…79021478001140367359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.265 Γ— 10⁹⁸(99-digit number)
42653455618911889551…58042956002280734719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.530 Γ— 10⁹⁸(99-digit number)
85306911237823779102…16085912004561469439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.706 Γ— 10⁹⁹(100-digit number)
17061382247564755820…32171824009122938879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.412 Γ— 10⁹⁹(100-digit number)
34122764495129511641…64343648018245877759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.824 Γ— 10⁹⁹(100-digit number)
68245528990259023282…28687296036491755519
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 2451567

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 ab3f64d86946590653eb8542963ef47e9d3b12511fcd9227d6b42f8838318198

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 #2,451,567 on Chainz β†—
Circulating Supply:58,009,697 XPMΒ·at block #6,845,655 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