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Block #20,102

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/12/2013, 10:58:03 AM Β· Difficulty 7.9296 Β· 6,787,129 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
94992a42bdb82a3a03688e933f3a4b6b16a8b26ef74a16553b437b3999cd307b
View on Chainz β†—

Height

#20,102

Difficulty

7.929562

Transactions

1

Size

199 B

Version

2

Bits

07edf7c5

Nonce

171

Timestamp

7/12/2013, 10:58:03 AM

Confirmations

6,787,129

Mined by

⛏️ P2SHAdWHv8yonFfCMPM3Ss72GYKPuZ8LoH1JaP

Merkle Root

eac61622f6c0f8f2699fea8a161d0a22f457736c52ba9c7f87d15185ff38f1c9
Transactions (1)
Coinbaseeac61622f6c0f8…d15185ff38f1c9
1 in β†’ 1 out15.8800 XPM108 B
AdWHv8yo…8LoH1JaP
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.

5.953 Γ— 10⁹⁢(97-digit number)
59537160699778100442…96115507777959210901
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
5.953 Γ— 10⁹⁢(97-digit number)
59537160699778100442…96115507777959210901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.190 Γ— 10⁹⁷(98-digit number)
11907432139955620088…92231015555918421801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.381 Γ— 10⁹⁷(98-digit number)
23814864279911240176…84462031111836843601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.762 Γ— 10⁹⁷(98-digit number)
47629728559822480353…68924062223673687201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.525 Γ— 10⁹⁷(98-digit number)
95259457119644960707…37848124447347374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.905 Γ— 10⁹⁸(99-digit number)
19051891423928992141…75696248894694748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.810 Γ— 10⁹⁸(99-digit number)
38103782847857984283…51392497789389497601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,701,864 XPMΒ·at block #6,807,230 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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