XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,739,735

Block #2,739,735

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/8/2018, 3:52:59 PM Β· Difficulty 11.6199 Β· 4,100,774 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3e0167a53c8a9399aa0fe2ed0007257955aa4b4ed096a9bedcbb3b0acb00a401
View on Chainz β†—

Difficulty

11.619883

Transactions

1

Size

200 B

Version

2

Bits

0b9eb0a6

Nonce

973,159,229

Timestamp

7/8/2018, 3:52:59 PM

Confirmations

4,100,774

Merkle Root

a05a08f22ad38f05584f91146cb7fa8bf6a1a0e3bac56912b5e326053b8dd8cc
Transactions (1)
Coinbasea05a08f22ad38f…e326053b8dd8cc
1 in β†’ 1 out7.3900 XPM110 B
AYQLgwUa…bKL8jfUv
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.

1.790 Γ— 10⁹⁴(95-digit number)
17901830689971474064…59205768776101993600
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
1.790 Γ— 10⁹⁴(95-digit number)
17901830689971474064…59205768776101993599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.580 Γ— 10⁹⁴(95-digit number)
35803661379942948128…18411537552203987199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.160 Γ— 10⁹⁴(95-digit number)
71607322759885896257…36823075104407974399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.432 Γ— 10⁹⁡(96-digit number)
14321464551977179251…73646150208815948799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.864 Γ— 10⁹⁡(96-digit number)
28642929103954358503…47292300417631897599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.728 Γ— 10⁹⁡(96-digit number)
57285858207908717006…94584600835263795199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.145 Γ— 10⁹⁢(97-digit number)
11457171641581743401…89169201670527590399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.291 Γ— 10⁹⁢(97-digit number)
22914343283163486802…78338403341055180799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.582 Γ— 10⁹⁢(97-digit number)
45828686566326973604…56676806682110361599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.165 Γ— 10⁹⁢(97-digit number)
91657373132653947209…13353613364220723199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.833 Γ— 10⁹⁷(98-digit number)
18331474626530789441…26707226728441446399
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 2739735

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 3e0167a53c8a9399aa0fe2ed0007257955aa4b4ed096a9bedcbb3b0acb00a401

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 #2,739,735 on Chainz β†—
Circulating Supply:57,968,399 XPMΒ·at block #6,840,508 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