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Home/Chain Registry/Block #1,668,605

Block #1,668,605

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/11/2016, 3:33:31 PM Β· Difficulty 10.6981 Β· 5,174,344 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bc273a3a5d1847861d44549611a87f4d499500a7c21b3ba03b26c9dbcf582170
View on Chainz β†—

Difficulty

10.698119

Transactions

1

Size

199 B

Version

2

Bits

0ab2b7e7

Nonce

1,859,936,473

Timestamp

7/11/2016, 3:33:31 PM

Confirmations

5,174,344

Merkle Root

ec2ea57653dd05363fe4568cdad83790846faa5e06626dd3cd2d1bd8d47b5b72
Transactions (1)
Coinbaseec2ea57653dd05…2d1bd8d47b5b72
1 in β†’ 1 out8.7200 XPM109 B
AJuBaot5…yHLjg1j8
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.

4.276 Γ— 10⁹⁡(96-digit number)
42761831696196477027…70539441054299207680
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
4.276 Γ— 10⁹⁡(96-digit number)
42761831696196477027…70539441054299207679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.552 Γ— 10⁹⁡(96-digit number)
85523663392392954055…41078882108598415359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.710 Γ— 10⁹⁢(97-digit number)
17104732678478590811…82157764217196830719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.420 Γ— 10⁹⁢(97-digit number)
34209465356957181622…64315528434393661439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.841 Γ— 10⁹⁢(97-digit number)
68418930713914363244…28631056868787322879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.368 Γ— 10⁹⁷(98-digit number)
13683786142782872648…57262113737574645759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.736 Γ— 10⁹⁷(98-digit number)
27367572285565745297…14524227475149291519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.473 Γ— 10⁹⁷(98-digit number)
54735144571131490595…29048454950298583039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.094 Γ— 10⁹⁸(99-digit number)
10947028914226298119…58096909900597166079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.189 Γ— 10⁹⁸(99-digit number)
21894057828452596238…16193819801194332159
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 1668605

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 bc273a3a5d1847861d44549611a87f4d499500a7c21b3ba03b26c9dbcf582170

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 #1,668,605 on Chainz β†—
Circulating Supply:57,987,943 XPMΒ·at block #6,842,948 Β· updates every 60s
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