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Home/Chain Registry/Block #2,147,140

Block #2,147,140

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/5/2017, 3:46:45 PM Β· Difficulty 10.8926 Β· 4,694,693 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d3ac8dca97cc91776115ab05d4f0faec5dfd4582755f52d043e1fe36b08c5913
View on Chainz β†—

Difficulty

10.892590

Transactions

1

Size

201 B

Version

2

Bits

0ae480c5

Nonce

646,619,060

Timestamp

6/5/2017, 3:46:45 PM

Confirmations

4,694,693

Merkle Root

bf9cc28012ccee923389968f1a9c352a336bd37bb88a48f01d8c8b8516506b05
Transactions (1)
Coinbasebf9cc28012ccee…8c8b8516506b05
1 in β†’ 1 out8.4100 XPM110 B
AdAi4tKv…qCtpaR1x
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.

3.295 Γ— 10⁹⁢(97-digit number)
32957940122817830216…81663313716949032960
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
3.295 Γ— 10⁹⁢(97-digit number)
32957940122817830216…81663313716949032959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.591 Γ— 10⁹⁢(97-digit number)
65915880245635660433…63326627433898065919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.318 Γ— 10⁹⁷(98-digit number)
13183176049127132086…26653254867796131839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.636 Γ— 10⁹⁷(98-digit number)
26366352098254264173…53306509735592263679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.273 Γ— 10⁹⁷(98-digit number)
52732704196508528346…06613019471184527359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.054 Γ— 10⁹⁸(99-digit number)
10546540839301705669…13226038942369054719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.109 Γ— 10⁹⁸(99-digit number)
21093081678603411338…26452077884738109439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.218 Γ— 10⁹⁸(99-digit number)
42186163357206822677…52904155769476218879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.437 Γ— 10⁹⁸(99-digit number)
84372326714413645354…05808311538952437759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.687 Γ— 10⁹⁹(100-digit number)
16874465342882729070…11616623077904875519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.374 Γ— 10⁹⁹(100-digit number)
33748930685765458141…23233246155809751039
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 2147140

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 d3ac8dca97cc91776115ab05d4f0faec5dfd4582755f52d043e1fe36b08c5913

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 #2,147,140 on Chainz β†—
Circulating Supply:57,979,037 XPMΒ·at block #6,841,832 Β· updates every 60s
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