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Home/Chain Registry/Block #2,735,943

Block #2,735,943

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/6/2018, 2:50:23 AM Β· Difficulty 11.6100 Β· 4,108,100 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
015db34c9d158192e1cbbbf269b2b73e5b0aa7329254f312d1f1975444505e7d
View on Chainz β†—

Difficulty

11.609965

Transactions

3

Size

798 B

Version

2

Bits

0b9c26ac

Nonce

73,597,511

Timestamp

7/6/2018, 2:50:23 AM

Confirmations

4,108,100

Merkle Root

1a6924dcbfd3145074e993dc660fb823008850e178f94f6b894205017ec63399
Transactions (3)
Coinbase189ee13ef7ed97…b0bfb041bae26e
1 in β†’ 1 out7.4300 XPM110 B
AZtxQr2F…7grUWrUz
3f7b4052b9d249…2ec3cdbd250f49
1 in β†’ 2 out4.7027 XPM226 B
AToyc9N9…8QdyNQrjAGeZ8NJn…ZBREQjik
eaf739ff8edd70…9941dabc21ebad
2 in β†’ 2 out4.0336 XPM372 B
AH2GDY9S…86G1xxUjALsMPjNH…Ta7qg3is
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.

6.410 Γ— 10⁹⁡(96-digit number)
64104610635431896015…86571017521565526240
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.410 Γ— 10⁹⁡(96-digit number)
64104610635431896015…86571017521565526241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.282 Γ— 10⁹⁢(97-digit number)
12820922127086379203…73142035043131052481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.564 Γ— 10⁹⁢(97-digit number)
25641844254172758406…46284070086262104961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.128 Γ— 10⁹⁢(97-digit number)
51283688508345516812…92568140172524209921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.025 Γ— 10⁹⁷(98-digit number)
10256737701669103362…85136280345048419841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.051 Γ— 10⁹⁷(98-digit number)
20513475403338206724…70272560690096839681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.102 Γ— 10⁹⁷(98-digit number)
41026950806676413449…40545121380193679361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.205 Γ— 10⁹⁷(98-digit number)
82053901613352826899…81090242760387358721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.641 Γ— 10⁹⁸(99-digit number)
16410780322670565379…62180485520774717441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.282 Γ— 10⁹⁸(99-digit number)
32821560645341130759…24360971041549434881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.564 Γ— 10⁹⁸(99-digit number)
65643121290682261519…48721942083098869761
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2735943

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 015db34c9d158192e1cbbbf269b2b73e5b0aa7329254f312d1f1975444505e7d

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 #2,735,943 on Chainz β†—
Circulating Supply:57,996,714 XPMΒ·at block #6,844,042 Β· updates every 60s
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