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Block #197,282

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/7/2013, 12:29:44 AM Β· Difficulty 9.8831 Β· 6,610,575 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6071039bfeae14fa1fd490178e67940bafd0c1aff5dddd8b389ca0f58800322a
View on Chainz β†—

Height

#197,282

Difficulty

9.883093

Transactions

1

Size

199 B

Version

2

Bits

09e2125b

Nonce

115,294

Timestamp

10/7/2013, 12:29:44 AM

Confirmations

6,610,575

Mined by

⛏️ P2SHAW5agYxrnDpfi7XV6pmmPv2p9yidUEFLUb

Merkle Root

d1ef113401c9ccb096a116c9deb1672e8a57ee19822ac99718b1d8d8d9db3dc6
Transactions (1)
Coinbased1ef113401c9cc…b1d8d8d9db3dc6
1 in β†’ 1 out10.2200 XPM109 B
AW5agYxr…idUEFLUb
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.

8.008 Γ— 10⁹⁴(95-digit number)
80080046374756156631…80950440919794496541
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
8.008 Γ— 10⁹⁴(95-digit number)
80080046374756156631…80950440919794496541
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.601 Γ— 10⁹⁡(96-digit number)
16016009274951231326…61900881839588993081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.203 Γ— 10⁹⁡(96-digit number)
32032018549902462652…23801763679177986161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.406 Γ— 10⁹⁡(96-digit number)
64064037099804925305…47603527358355972321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.281 Γ— 10⁹⁢(97-digit number)
12812807419960985061…95207054716711944641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.562 Γ— 10⁹⁢(97-digit number)
25625614839921970122…90414109433423889281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.125 Γ— 10⁹⁢(97-digit number)
51251229679843940244…80828218866847778561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.025 Γ— 10⁹⁷(98-digit number)
10250245935968788048…61656437733695557121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.050 Γ— 10⁹⁷(98-digit number)
20500491871937576097…23312875467391114241
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:57,706,894 XPMΒ·at block #6,807,856 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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