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Block #61,143

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 11:48:14 AM Β· Difficulty 8.9720 Β· 6,744,057 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
82ab8872b93b5e431c7321dd0658460c2b4a87fbcb8ef901b7a434c8fd62624f
View on Chainz β†—

Height

#61,143

Difficulty

8.972002

Transactions

1

Size

204 B

Version

2

Bits

08f8d522

Nonce

467

Timestamp

7/18/2013, 11:48:14 AM

Confirmations

6,744,057

Mined by

⛏️ P2SHAV3Mx3AqCBr85EUqewYnyDKYAdAKiwER2W

Merkle Root

2ce787a0460e85e83d2151d579fe3cdf95ddf3e1aade5bbc4847039b1716dcd8
Transactions (1)
Coinbase2ce787a0460e85…47039b1716dcd8
1 in β†’ 1 out12.4100 XPM110 B
AV3Mx3Aq…AKiwER2W
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.

2.815 Γ— 10¹⁰³(104-digit number)
28150763139259940055…06009052770725701251
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
2.815 Γ— 10¹⁰³(104-digit number)
28150763139259940055…06009052770725701251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.630 Γ— 10¹⁰³(104-digit number)
56301526278519880110…12018105541451402501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.126 Γ— 10¹⁰⁴(105-digit number)
11260305255703976022…24036211082902805001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.252 Γ— 10¹⁰⁴(105-digit number)
22520610511407952044…48072422165805610001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.504 Γ— 10¹⁰⁴(105-digit number)
45041221022815904088…96144844331611220001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.008 Γ— 10¹⁰⁴(105-digit number)
90082442045631808176…92289688663222440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.801 Γ— 10¹⁰⁡(106-digit number)
18016488409126361635…84579377326444880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.603 Γ— 10¹⁰⁡(106-digit number)
36032976818252723270…69158754652889760001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,685,670 XPMΒ·at block #6,805,199 Β· updates every 60s
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