XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,759,859

Block #2,759,859

1CCLength 13β˜…β˜…β˜…β˜…β˜…

Cunningham Chain of the First Kind Β· Discovered 7/22/2018, 6:21:57 AM Β· Difficulty 11.6589 Β· 4,077,254 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
868e499a6028e4a765835d142b0077401acc4442dc64e119dab5decc0feca4f6
View on Chainz β†—

Difficulty

11.658921

Transactions

2

Size

390 B

Version

2

Bits

0ba8af08

Nonce

1,355,588,456

Timestamp

7/22/2018, 6:21:57 AM

Confirmations

4,077,254

Merkle Root

d890fc654e409edd8741f9ed9b41a4b4dd910363a57509fe12a63aa31836b5f4
Transactions (2)
Coinbase0e1d053663d930…0ef6a12b2f136c
1 in β†’ 1 out7.3500 XPM109 B
AZtxQr2F…7grUWrUz
f2d65ab61cb868…b99119b607fb10
1 in β†’ 2 out7.3300 XPM192 B
Ack1CHDE…QdxM6gUyAdGFnV3a…o6n2zX3x
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.

1.744 Γ— 10⁹²(93-digit number)
17449497346527836504…58139071674499174200
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
1.744 Γ— 10⁹²(93-digit number)
17449497346527836504…58139071674499174199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.489 Γ— 10⁹²(93-digit number)
34898994693055673009…16278143348998348399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.979 Γ— 10⁹²(93-digit number)
69797989386111346018…32556286697996696799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.395 Γ— 10⁹³(94-digit number)
13959597877222269203…65112573395993393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.791 Γ— 10⁹³(94-digit number)
27919195754444538407…30225146791986787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.583 Γ— 10⁹³(94-digit number)
55838391508889076814…60450293583973574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.116 Γ— 10⁹⁴(95-digit number)
11167678301777815362…20900587167947148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.233 Γ— 10⁹⁴(95-digit number)
22335356603555630725…41801174335894297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.467 Γ— 10⁹⁴(95-digit number)
44670713207111261451…83602348671788595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.934 Γ— 10⁹⁴(95-digit number)
89341426414222522903…67204697343577190399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.786 Γ— 10⁹⁡(96-digit number)
17868285282844504580…34409394687154380799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
3.573 Γ— 10⁹⁡(96-digit number)
35736570565689009161…68818789374308761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
13
2^12 Γ— origin βˆ’ 1
7.147 Γ— 10⁹⁡(96-digit number)
71473141131378018323…37637578748617523199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 13 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
LegendaryChain length 13
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 2759859

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 868e499a6028e4a765835d142b0077401acc4442dc64e119dab5decc0feca4f6

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 #2,759,859 on Chainz β†—
Circulating Supply:57,941,211 XPMΒ·at block #6,837,112 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