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Block #169,527

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/18/2013, 2:13:40 AM Β· Difficulty 9.8674 Β· 6,673,489 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a7981fb0fcb76ee80717189f75cf3629dbe3f90d16cbb8f589f0fdf1856bff0d
View on Chainz β†—

Height

#169,527

Difficulty

9.867443

Transactions

1

Size

203 B

Version

2

Bits

09de10be

Nonce

50,331,686

Timestamp

9/18/2013, 2:13:40 AM

Confirmations

6,673,489

Merkle Root

22c65353a6e0b263428ff5780c4e7e9035a05c7d348418131c2c7b76121ac8cd
Transactions (1)
Coinbase22c65353a6e0b2…2c7b76121ac8cd
1 in β†’ 1 out10.2600 XPM112 B
AcLBm5Z9…S683d7c3
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.

1.480 Γ— 10⁹⁢(97-digit number)
14800392284760305026…34322051161817084160
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.480 Γ— 10⁹⁢(97-digit number)
14800392284760305026…34322051161817084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.960 Γ— 10⁹⁢(97-digit number)
29600784569520610052…68644102323634168321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.920 Γ— 10⁹⁢(97-digit number)
59201569139041220104…37288204647268336641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.184 Γ— 10⁹⁷(98-digit number)
11840313827808244020…74576409294536673281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.368 Γ— 10⁹⁷(98-digit number)
23680627655616488041…49152818589073346561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.736 Γ— 10⁹⁷(98-digit number)
47361255311232976083…98305637178146693121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.472 Γ— 10⁹⁷(98-digit number)
94722510622465952166…96611274356293386241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.894 Γ— 10⁹⁸(99-digit number)
18944502124493190433…93222548712586772481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.788 Γ— 10⁹⁸(99-digit number)
37889004248986380866…86445097425173544961
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 169527

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 a7981fb0fcb76ee80717189f75cf3629dbe3f90d16cbb8f589f0fdf1856bff0d

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 #169,527 on Chainz β†—
Circulating Supply:57,988,484 XPMΒ·at block #6,843,015 Β· updates every 60s
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