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Home/Chain Registry/Block #2,737,128

Block #2,737,128

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/6/2018, 10:48:35 PM Β· Difficulty 11.6089 Β· 4,106,008 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
be284aa9da2e2b003a08d1b698054320c48f85b6473bf4263d5be7a93a30db35
View on Chainz β†—

Difficulty

11.608893

Transactions

2

Size

718 B

Version

2

Bits

0b9be06d

Nonce

1,926,315,474

Timestamp

7/6/2018, 10:48:35 PM

Confirmations

4,106,008

Merkle Root

7f120a0a995b61bb56a17ca6649bdbe342d596d7ea43eba38292bf44e1c065a0
Transactions (2)
Coinbasec1e21128c093d4…fc769a89cd17e5
1 in β†’ 1 out7.4200 XPM110 B
ASRD46A9…WipdxSTL
5dc02bc20c38c6…1f8c1db49aab5e
3 in β†’ 2 out788.0220 XPM519 B
AHzkHzeK…3wME2gBFAWsDNS1F…RN691ToV
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.

1.877 Γ— 10⁹²(93-digit number)
18777856044685632491…89875907352289131400
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
1.877 Γ— 10⁹²(93-digit number)
18777856044685632491…89875907352289131401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.755 Γ— 10⁹²(93-digit number)
37555712089371264982…79751814704578262801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.511 Γ— 10⁹²(93-digit number)
75111424178742529964…59503629409156525601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.502 Γ— 10⁹³(94-digit number)
15022284835748505992…19007258818313051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.004 Γ— 10⁹³(94-digit number)
30044569671497011985…38014517636626102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.008 Γ— 10⁹³(94-digit number)
60089139342994023971…76029035273252204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.201 Γ— 10⁹⁴(95-digit number)
12017827868598804794…52058070546504409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.403 Γ— 10⁹⁴(95-digit number)
24035655737197609588…04116141093008819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.807 Γ— 10⁹⁴(95-digit number)
48071311474395219177…08232282186017638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.614 Γ— 10⁹⁴(95-digit number)
96142622948790438354…16464564372035276801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.922 Γ— 10⁹⁡(96-digit number)
19228524589758087670…32929128744070553601
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 2737128

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 be284aa9da2e2b003a08d1b698054320c48f85b6473bf4263d5be7a93a30db35

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 #2,737,128 on Chainz β†—
Circulating Supply:57,989,452 XPMΒ·at block #6,843,135 Β· updates every 60s
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