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Block #180,758

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/26/2013, 1:28:06 AM Β· Difficulty 9.8616 Β· 6,615,178 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
938fdb3867f715f8d789b69ddc7bcdc51bd1ab04bbde56beab9b62b5d6baa697
View on Chainz β†—

Height

#180,758

Difficulty

9.861583

Transactions

1

Size

198 B

Version

2

Bits

09dc90b5

Nonce

25,172

Timestamp

9/26/2013, 1:28:06 AM

Confirmations

6,615,178

Merkle Root

ae551d1b38f6ad2e99f15205c5511510c32e8287e1dcf42e5ea4970971cbf8cd
Transactions (1)
Coinbaseae551d1b38f6ad…a4970971cbf8cd
1 in β†’ 1 out10.2700 XPM109 B
AP9Q5TCM…n3e5pxk8
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.

4.039 Γ— 10⁹³(94-digit number)
40395223815451734905…58397752722152303700
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
4.039 Γ— 10⁹³(94-digit number)
40395223815451734905…58397752722152303701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.079 Γ— 10⁹³(94-digit number)
80790447630903469810…16795505444304607401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.615 Γ— 10⁹⁴(95-digit number)
16158089526180693962…33591010888609214801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.231 Γ— 10⁹⁴(95-digit number)
32316179052361387924…67182021777218429601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.463 Γ— 10⁹⁴(95-digit number)
64632358104722775848…34364043554436859201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.292 Γ— 10⁹⁡(96-digit number)
12926471620944555169…68728087108873718401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.585 Γ— 10⁹⁡(96-digit number)
25852943241889110339…37456174217747436801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.170 Γ— 10⁹⁡(96-digit number)
51705886483778220678…74912348435494873601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.034 Γ— 10⁹⁢(97-digit number)
10341177296755644135…49824696870989747201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.068 Γ— 10⁹⁢(97-digit number)
20682354593511288271…99649393741979494401
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 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
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 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 180758

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 938fdb3867f715f8d789b69ddc7bcdc51bd1ab04bbde56beab9b62b5d6baa697

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 #180,758 on Chainz β†—
Circulating Supply:57,611,577 XPMΒ·at block #6,795,935 Β· updates every 60s
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