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Home/Chain Registry/Block #2,077,197

Block #2,077,197

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/19/2017, 5:19:34 AM Β· Difficulty 10.8484 Β· 4,759,519 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b155546beaf5e8654c48be973b2faa05501658a092ac36e966868b6d4251a62a
View on Chainz β†—

Difficulty

10.848368

Transactions

1

Size

199 B

Version

2

Bits

0ad92ea0

Nonce

1,053,469,287

Timestamp

4/19/2017, 5:19:34 AM

Confirmations

4,759,519

Merkle Root

2b340abeb82b50149726e2abc8afe306d6ca93d91e87af385acd79a3fa1f2708
Transactions (1)
Coinbase2b340abeb82b50…cd79a3fa1f2708
1 in β†’ 1 out8.4800 XPM109 B
APnU4MmE…R28kGrwq
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.

6.689 Γ— 10⁹³(94-digit number)
66895631439771772172…75120365570716874240
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
6.689 Γ— 10⁹³(94-digit number)
66895631439771772172…75120365570716874239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.337 Γ— 10⁹⁴(95-digit number)
13379126287954354434…50240731141433748479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.675 Γ— 10⁹⁴(95-digit number)
26758252575908708868…00481462282867496959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.351 Γ— 10⁹⁴(95-digit number)
53516505151817417737…00962924565734993919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.070 Γ— 10⁹⁡(96-digit number)
10703301030363483547…01925849131469987839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.140 Γ— 10⁹⁡(96-digit number)
21406602060726967095…03851698262939975679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.281 Γ— 10⁹⁡(96-digit number)
42813204121453934190…07703396525879951359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.562 Γ— 10⁹⁡(96-digit number)
85626408242907868380…15406793051759902719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.712 Γ— 10⁹⁢(97-digit number)
17125281648581573676…30813586103519805439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.425 Γ— 10⁹⁢(97-digit number)
34250563297163147352…61627172207039610879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2077197

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 b155546beaf5e8654c48be973b2faa05501658a092ac36e966868b6d4251a62a

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 #2,077,197 on Chainz β†—
Circulating Supply:57,938,010 XPMΒ·at block #6,836,715 Β· updates every 60s
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