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Block #168,208

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/17/2013, 3:48:29 AM Β· Difficulty 9.8681 Β· 6,658,936 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9547f0be6aa1a286d4b0c411b2a22c314cff71c149f3867bdf6ec368230bae43
View on Chainz β†—

Height

#168,208

Difficulty

9.868098

Transactions

1

Size

198 B

Version

2

Bits

09de3bb0

Nonce

212,860

Timestamp

9/17/2013, 3:48:29 AM

Confirmations

6,658,936

Merkle Root

b22c1ad7e630af36b1a8ae935971b8f765a52696a498ea221b84f8312bf50c96
Transactions (1)
Coinbaseb22c1ad7e630af…84f8312bf50c96
1 in β†’ 1 out10.2500 XPM109 B
AXcstvw2…TmnmzdbL
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.

1.904 Γ— 10⁹³(94-digit number)
19045063217309221932…25616570727865648850
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
1.904 Γ— 10⁹³(94-digit number)
19045063217309221932…25616570727865648849
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.809 Γ— 10⁹³(94-digit number)
38090126434618443864…51233141455731297699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.618 Γ— 10⁹³(94-digit number)
76180252869236887729…02466282911462595399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.523 Γ— 10⁹⁴(95-digit number)
15236050573847377545…04932565822925190799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.047 Γ— 10⁹⁴(95-digit number)
30472101147694755091…09865131645850381599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.094 Γ— 10⁹⁴(95-digit number)
60944202295389510183…19730263291700763199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.218 Γ— 10⁹⁡(96-digit number)
12188840459077902036…39460526583401526399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.437 Γ— 10⁹⁡(96-digit number)
24377680918155804073…78921053166803052799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.875 Γ— 10⁹⁡(96-digit number)
48755361836311608146…57842106333606105599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 168208

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 9547f0be6aa1a286d4b0c411b2a22c314cff71c149f3867bdf6ec368230bae43

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 #168,208 on Chainz β†—
Circulating Supply:57,861,334 XPMΒ·at block #6,827,143 Β· updates every 60s
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