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Block #60,655

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 9:12:21 AM Β· Difficulty 8.9701 Β· 6,734,727 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
68d145ad0eae64f3ad94d20e47d9d095cdac42d7d59877096092c117b23b6cd4
View on Chainz β†—

Height

#60,655

Difficulty

8.970079

Transactions

1

Size

198 B

Version

2

Bits

08f85721

Nonce

19

Timestamp

7/18/2013, 9:12:21 AM

Confirmations

6,734,727

Mined by

⛏️ P2SHAeTcmmqHMYEKBSfvTp4dmwQ4JaLrFchfe1

Merkle Root

1ac6b9c7586f84bb550e83eae62e0ad23d7c72379d035ca44824aa55cff22f81
Transactions (1)
Coinbase1ac6b9c7586f84…24aa55cff22f81
1 in β†’ 1 out12.4100 XPM110 B
AeTcmmqH…LrFchfe1
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.

1.057 Γ— 10⁸⁹(90-digit number)
10576397836112950564…44520405010401548501
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
1.057 Γ— 10⁸⁹(90-digit number)
10576397836112950564…44520405010401548501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.115 Γ— 10⁸⁹(90-digit number)
21152795672225901128…89040810020803097001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.230 Γ— 10⁸⁹(90-digit number)
42305591344451802256…78081620041606194001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.461 Γ— 10⁸⁹(90-digit number)
84611182688903604512…56163240083212388001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.692 Γ— 10⁹⁰(91-digit number)
16922236537780720902…12326480166424776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.384 Γ— 10⁹⁰(91-digit number)
33844473075561441805…24652960332849552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.768 Γ— 10⁹⁰(91-digit number)
67688946151122883610…49305920665699104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.353 Γ— 10⁹¹(92-digit number)
13537789230224576722…98611841331398208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.707 Γ— 10⁹¹(92-digit number)
27075578460449153444…97223682662796416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.415 Γ— 10⁹¹(92-digit number)
54151156920898306888…94447365325592832001
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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,607,115 XPMΒ·at block #6,795,381 Β· updates every 60s
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