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Home/Chain Registry/Block #1,682,108

Block #1,682,108

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 6:52:05 PM Β· Difficulty 10.7186 Β· 5,149,481 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f4b0a808093f04b8d94c8821bd293e4ddd32e4092f5c7fd10ef63f8b3a8f699f
View on Chainz β†—

Difficulty

10.718575

Transactions

1

Size

200 B

Version

2

Bits

0ab7f484

Nonce

291,026,551

Timestamp

7/20/2016, 6:52:05 PM

Confirmations

5,149,481

Merkle Root

b1e746908d7cdafa684acab88cd625e1ba6b0ff439eb4f26956943feca33843c
Transactions (1)
Coinbaseb1e746908d7cda…6943feca33843c
1 in β†’ 1 out8.6900 XPM109 B
AXeRcdya…LWNNRTUd
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.

3.287 Γ— 10⁹⁢(97-digit number)
32876116860244061281…10803679293347557760
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
3.287 Γ— 10⁹⁢(97-digit number)
32876116860244061281…10803679293347557759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.575 Γ— 10⁹⁢(97-digit number)
65752233720488122562…21607358586695115519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.315 Γ— 10⁹⁷(98-digit number)
13150446744097624512…43214717173390231039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.630 Γ— 10⁹⁷(98-digit number)
26300893488195249024…86429434346780462079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.260 Γ— 10⁹⁷(98-digit number)
52601786976390498049…72858868693560924159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.052 Γ— 10⁹⁸(99-digit number)
10520357395278099609…45717737387121848319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.104 Γ— 10⁹⁸(99-digit number)
21040714790556199219…91435474774243696639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.208 Γ— 10⁹⁸(99-digit number)
42081429581112398439…82870949548487393279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.416 Γ— 10⁹⁸(99-digit number)
84162859162224796879…65741899096974786559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.683 Γ— 10⁹⁹(100-digit number)
16832571832444959375…31483798193949573119
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 1682108

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 f4b0a808093f04b8d94c8821bd293e4ddd32e4092f5c7fd10ef63f8b3a8f699f

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 #1,682,108 on Chainz β†—
Circulating Supply:57,896,809 XPMΒ·at block #6,831,588 Β· updates every 60s
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