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Home/Chain Registry/Block #2,772,499

Block #2,772,499

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/31/2018, 12:17:23 AM Β· Difficulty 11.6624 Β· 4,070,578 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ba88f2e18914085bc8b9401abf182fb3154a1e34a574bc2b010a4c2125dcfa20
View on Chainz β†—

Difficulty

11.662372

Transactions

1

Size

199 B

Version

2

Bits

0ba99138

Nonce

1,449,815,680

Timestamp

7/31/2018, 12:17:23 AM

Confirmations

4,070,578

Merkle Root

f1c8240c6790e72813ec8b127d0b0049e5d20d034bab1e3e65bc652a7900fe2a
Transactions (1)
Coinbasef1c8240c6790e7…bc652a7900fe2a
1 in β†’ 1 out7.3400 XPM110 B
AcmA5CZQ…niujUhSq
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.

9.360 Γ— 10⁹²(93-digit number)
93604724543217919464…49832795894956298240
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
9.360 Γ— 10⁹²(93-digit number)
93604724543217919464…49832795894956298239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.872 Γ— 10⁹³(94-digit number)
18720944908643583892…99665591789912596479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.744 Γ— 10⁹³(94-digit number)
37441889817287167785…99331183579825192959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.488 Γ— 10⁹³(94-digit number)
74883779634574335571…98662367159650385919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.497 Γ— 10⁹⁴(95-digit number)
14976755926914867114…97324734319300771839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.995 Γ— 10⁹⁴(95-digit number)
29953511853829734228…94649468638601543679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.990 Γ— 10⁹⁴(95-digit number)
59907023707659468457…89298937277203087359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.198 Γ— 10⁹⁡(96-digit number)
11981404741531893691…78597874554406174719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.396 Γ— 10⁹⁡(96-digit number)
23962809483063787383…57195749108812349439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.792 Γ— 10⁹⁡(96-digit number)
47925618966127574766…14391498217624698879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.585 Γ— 10⁹⁡(96-digit number)
95851237932255149532…28782996435249397759
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 2772499

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 ba88f2e18914085bc8b9401abf182fb3154a1e34a574bc2b010a4c2125dcfa20

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 #2,772,499 on Chainz β†—
Circulating Supply:57,988,976 XPMΒ·at block #6,843,076 Β· updates every 60s
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