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Block #170,168

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/18/2013, 2:01:45 PM Β· Difficulty 9.8657 Β· 6,656,450 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
305483955a92f395c8e351f6ef5d17b1caf24a61e9914198238f4e2a0fd40d61
View on Chainz β†—

Height

#170,168

Difficulty

9.865741

Transactions

1

Size

201 B

Version

2

Bits

09dda134

Nonce

130,987

Timestamp

9/18/2013, 2:01:45 PM

Confirmations

6,656,450

Merkle Root

1c6c3436d696ad1d51504eeebbc120734e3dcbc9d270b02f31ceb456126d8718
Transactions (1)
Coinbase1c6c3436d696ad…ceb456126d8718
1 in β†’ 1 out10.2600 XPM110 B
AUVL3hJW…9tpY77QD
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.

6.325 Γ— 10⁹⁡(96-digit number)
63255164141243682403…46898578378162292800
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
6.325 Γ— 10⁹⁡(96-digit number)
63255164141243682403…46898578378162292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.265 Γ— 10⁹⁢(97-digit number)
12651032828248736480…93797156756324585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.530 Γ— 10⁹⁢(97-digit number)
25302065656497472961…87594313512649171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.060 Γ— 10⁹⁢(97-digit number)
50604131312994945922…75188627025298342399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.012 Γ— 10⁹⁷(98-digit number)
10120826262598989184…50377254050596684799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.024 Γ— 10⁹⁷(98-digit number)
20241652525197978369…00754508101193369599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.048 Γ— 10⁹⁷(98-digit number)
40483305050395956738…01509016202386739199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.096 Γ— 10⁹⁷(98-digit number)
80966610100791913476…03018032404773478399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.619 Γ— 10⁹⁸(99-digit number)
16193322020158382695…06036064809546956799
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 170168

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 305483955a92f395c8e351f6ef5d17b1caf24a61e9914198238f4e2a0fd40d61

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 #170,168 on Chainz β†—
Circulating Supply:57,857,097 XPMΒ·at block #6,826,617 Β· updates every 60s
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