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Block #180,869

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/26/2013, 3:41:52 AM Β· Difficulty 9.8610 Β· 6,635,950 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
408b9c9d9a0f58793645a622c8b32b980aa0d4bd2e2d51bd83370d11ab8f75fc
View on Chainz β†—

Height

#180,869

Difficulty

9.860962

Transactions

1

Size

201 B

Version

2

Bits

09dc6807

Nonce

19,080

Timestamp

9/26/2013, 3:41:52 AM

Confirmations

6,635,950

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

316ac1e84e8b5d91ef2f85125f630c1e1022a8e76a719a2d5ac0412f280d6142
Transactions (1)
Coinbase316ac1e84e8b5d…c0412f280d6142
1 in β†’ 1 out10.2700 XPM109 B
AWbQMT1U…8Pt4ow7J
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.

6.848 Γ— 10⁹⁹(100-digit number)
68488731262132135003…15926067714297205761
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
6.848 Γ— 10⁹⁹(100-digit number)
68488731262132135003…15926067714297205761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.369 Γ— 10¹⁰⁰(101-digit number)
13697746252426427000…31852135428594411521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.739 Γ— 10¹⁰⁰(101-digit number)
27395492504852854001…63704270857188823041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.479 Γ— 10¹⁰⁰(101-digit number)
54790985009705708003…27408541714377646081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.095 Γ— 10¹⁰¹(102-digit number)
10958197001941141600…54817083428755292161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.191 Γ— 10¹⁰¹(102-digit number)
21916394003882283201…09634166857510584321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.383 Γ— 10¹⁰¹(102-digit number)
43832788007764566402…19268333715021168641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.766 Γ— 10¹⁰¹(102-digit number)
87665576015529132804…38536667430042337281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.753 Γ— 10¹⁰²(103-digit number)
17533115203105826560…77073334860084674561
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,778,591 XPMΒ·at block #6,816,818 Β· updates every 60s
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