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Block #161,081

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2013, 10:06:02 AM Β· Difficulty 9.8596 Β· 6,635,537 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fbbf5ca4008c94db9042dd0e2b9789b7a208dbb49d4032e7b94c3b6e1c3cac8b
View on Chainz β†—

Height

#161,081

Difficulty

9.859565

Transactions

1

Size

199 B

Version

2

Bits

09dc0c77

Nonce

318,725

Timestamp

9/12/2013, 10:06:02 AM

Confirmations

6,635,537

Merkle Root

aa231c9d4d38d8d4b842b8d609ee2ba4b49a1384fcf6476dbc7c0d60b6c71b2f
Transactions (1)
Coinbaseaa231c9d4d38d8…7c0d60b6c71b2f
1 in β†’ 1 out10.2700 XPM109 B
AVTdASf7…wQZLqRtu
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.

4.623 Γ— 10⁹³(94-digit number)
46235511042326360611…45195938294796604800
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
4.623 Γ— 10⁹³(94-digit number)
46235511042326360611…45195938294796604801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.247 Γ— 10⁹³(94-digit number)
92471022084652721222…90391876589593209601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.849 Γ— 10⁹⁴(95-digit number)
18494204416930544244…80783753179186419201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.698 Γ— 10⁹⁴(95-digit number)
36988408833861088489…61567506358372838401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.397 Γ— 10⁹⁴(95-digit number)
73976817667722176978…23135012716745676801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.479 Γ— 10⁹⁡(96-digit number)
14795363533544435395…46270025433491353601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.959 Γ— 10⁹⁡(96-digit number)
29590727067088870791…92540050866982707201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.918 Γ— 10⁹⁡(96-digit number)
59181454134177741582…85080101733965414401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.183 Γ— 10⁹⁢(97-digit number)
11836290826835548316…70160203467930828801
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 161081

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 fbbf5ca4008c94db9042dd0e2b9789b7a208dbb49d4032e7b94c3b6e1c3cac8b

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 #161,081 on Chainz β†—
Circulating Supply:57,616,942 XPMΒ·at block #6,796,617 Β· updates every 60s
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