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Home/Chain Registry/Block #2,655,695

Block #2,655,695

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/10/2018, 9:45:56 AM Β· Difficulty 11.7031 Β· 4,185,773 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2b969a08d58d8ae6095dc6c8b7176fa4c964ffdc92e23dba1e741014d1ecc96a
View on Chainz β†—

Difficulty

11.703099

Transactions

1

Size

201 B

Version

2

Bits

0bb3fe48

Nonce

207,665,630

Timestamp

5/10/2018, 9:45:56 AM

Confirmations

4,185,773

Merkle Root

d579da383d14c5aba65950cd4d0e2069613e87829106ea5bd1f18fb25f1877fb
Transactions (1)
Coinbased579da383d14c5…f18fb25f1877fb
1 in β†’ 1 out7.2900 XPM110 B
AXDXDRP5…RNUsmgNW
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.

1.074 Γ— 10⁹⁷(98-digit number)
10742344759449075571…07307485260802560000
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
1.074 Γ— 10⁹⁷(98-digit number)
10742344759449075571…07307485260802559999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.148 Γ— 10⁹⁷(98-digit number)
21484689518898151143…14614970521605119999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.296 Γ— 10⁹⁷(98-digit number)
42969379037796302286…29229941043210239999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.593 Γ— 10⁹⁷(98-digit number)
85938758075592604573…58459882086420479999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.718 Γ— 10⁹⁸(99-digit number)
17187751615118520914…16919764172840959999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.437 Γ— 10⁹⁸(99-digit number)
34375503230237041829…33839528345681919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.875 Γ— 10⁹⁸(99-digit number)
68751006460474083658…67679056691363839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.375 Γ— 10⁹⁹(100-digit number)
13750201292094816731…35358113382727679999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.750 Γ— 10⁹⁹(100-digit number)
27500402584189633463…70716226765455359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.500 Γ— 10⁹⁹(100-digit number)
55000805168379266927…41432453530910719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.100 Γ— 10¹⁰⁰(101-digit number)
11000161033675853385…82864907061821439999
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 2655695

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 2b969a08d58d8ae6095dc6c8b7176fa4c964ffdc92e23dba1e741014d1ecc96a

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 #2,655,695 on Chainz β†—
Circulating Supply:57,976,118 XPMΒ·at block #6,841,467 Β· updates every 60s
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