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Home/Chain Registry/Block #2,093,693

Block #2,093,693

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2017, 2:56:42 AM Β· Difficulty 10.8711 Β· 4,733,476 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f24e61fc5ab7369d50e38e883ef4a7b8dec00d1e6a01892d2305ae22513e83c7
View on Chainz β†—

Difficulty

10.871085

Transactions

1

Size

200 B

Version

2

Bits

0adeff6f

Nonce

625,012,690

Timestamp

4/30/2017, 2:56:42 AM

Confirmations

4,733,476

Merkle Root

16f4233ba5fc1fdc6e55dc1fd73936c8df0edc96ddd670085e00033d33569709
Transactions (1)
Coinbase16f4233ba5fc1f…00033d33569709
1 in β†’ 1 out8.4500 XPM110 B
AP5ErVLp…GQWEZUB6
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.

1.173 Γ— 10⁹⁴(95-digit number)
11738268758617432055…86309753410738990080
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
1.173 Γ— 10⁹⁴(95-digit number)
11738268758617432055…86309753410738990079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.347 Γ— 10⁹⁴(95-digit number)
23476537517234864110…72619506821477980159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.695 Γ— 10⁹⁴(95-digit number)
46953075034469728220…45239013642955960319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.390 Γ— 10⁹⁴(95-digit number)
93906150068939456441…90478027285911920639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.878 Γ— 10⁹⁡(96-digit number)
18781230013787891288…80956054571823841279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.756 Γ— 10⁹⁡(96-digit number)
37562460027575782576…61912109143647682559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.512 Γ— 10⁹⁡(96-digit number)
75124920055151565153…23824218287295365119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.502 Γ— 10⁹⁢(97-digit number)
15024984011030313030…47648436574590730239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.004 Γ— 10⁹⁢(97-digit number)
30049968022060626061…95296873149181460479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.009 Γ— 10⁹⁢(97-digit number)
60099936044121252122…90593746298362920959
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 2093693

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 f24e61fc5ab7369d50e38e883ef4a7b8dec00d1e6a01892d2305ae22513e83c7

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 #2,093,693 on Chainz β†—
Circulating Supply:57,861,448 XPMΒ·at block #6,827,168 Β· updates every 60s
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