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Home/Chain Registry/Block #2,726,967

Block #2,726,967

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/29/2018, 5:15:47 PM Β· Difficulty 11.6276 Β· 4,117,111 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
49cdfc81e6f361b1f2265450f7e2b133aba1da3ac6f26962e435b6573c86950d
View on Chainz β†—

Difficulty

11.627574

Transactions

1

Size

199 B

Version

2

Bits

0ba0a8b0

Nonce

567,109,130

Timestamp

6/29/2018, 5:15:47 PM

Confirmations

4,117,111

Merkle Root

cdf10579444d56ae7145f9d0b1da1e720662607a824207ce5e627f88384ea605
Transactions (1)
Coinbasecdf10579444d56…627f88384ea605
1 in β†’ 1 out7.3800 XPM110 B
AHzRWqSH…M6GHVoU2
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.

4.906 Γ— 10⁹²(93-digit number)
49064507536409372360…68002638766805113650
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
4.906 Γ— 10⁹²(93-digit number)
49064507536409372360…68002638766805113649
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.812 Γ— 10⁹²(93-digit number)
98129015072818744721…36005277533610227299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.962 Γ— 10⁹³(94-digit number)
19625803014563748944…72010555067220454599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.925 Γ— 10⁹³(94-digit number)
39251606029127497888…44021110134440909199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.850 Γ— 10⁹³(94-digit number)
78503212058254995777…88042220268881818399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.570 Γ— 10⁹⁴(95-digit number)
15700642411650999155…76084440537763636799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.140 Γ— 10⁹⁴(95-digit number)
31401284823301998310…52168881075527273599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.280 Γ— 10⁹⁴(95-digit number)
62802569646603996621…04337762151054547199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.256 Γ— 10⁹⁡(96-digit number)
12560513929320799324…08675524302109094399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.512 Γ— 10⁹⁡(96-digit number)
25121027858641598648…17351048604218188799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.024 Γ— 10⁹⁡(96-digit number)
50242055717283197297…34702097208436377599
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 2726967

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 49cdfc81e6f361b1f2265450f7e2b133aba1da3ac6f26962e435b6573c86950d

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 #2,726,967 on Chainz β†—
Circulating Supply:57,996,998 XPMΒ·at block #6,844,077 Β· updates every 60s
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