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Block #2,713,619

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/20/2018, 3:15:13 PM Β· Difficulty 11.6068 Β· 4,128,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
47f25f109e8d416c67c5072f73d16402f78fe71f5d9787fb764cb42f1959e4a0
View on Chainz β†—

Height

#2,713,619

Difficulty

11.606794

Transactions

1

Size

200 B

Version

2

Bits

0b9b56d9

Nonce

162,679,853

Timestamp

6/20/2018, 3:15:13 PM

Confirmations

4,128,876

Mined by

⛏️ P2SHAHVayoPie92Ae9Cv6ePjcsBh1suaP8CjUH

Merkle Root

8f69cf9af40e754624da5f5b221561b914dfdcbf7d90e3badd8e1df0c9b4bb7a
Transactions (1)
Coinbase8f69cf9af40e75…8e1df0c9b4bb7a
1 in β†’ 1 out7.4100 XPM110 B
AHVayoPi…uaP8CjUH
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.

2.097 Γ— 10⁹⁴(95-digit number)
20972674233188285058…47621514658885978561
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
2.097 Γ— 10⁹⁴(95-digit number)
20972674233188285058…47621514658885978561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.194 Γ— 10⁹⁴(95-digit number)
41945348466376570116…95243029317771957121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.389 Γ— 10⁹⁴(95-digit number)
83890696932753140233…90486058635543914241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.677 Γ— 10⁹⁡(96-digit number)
16778139386550628046…80972117271087828481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.355 Γ— 10⁹⁡(96-digit number)
33556278773101256093…61944234542175656961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.711 Γ— 10⁹⁡(96-digit number)
67112557546202512187…23888469084351313921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.342 Γ— 10⁹⁢(97-digit number)
13422511509240502437…47776938168702627841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.684 Γ— 10⁹⁢(97-digit number)
26845023018481004874…95553876337405255681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.369 Γ— 10⁹⁢(97-digit number)
53690046036962009749…91107752674810511361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.073 Γ— 10⁹⁷(98-digit number)
10738009207392401949…82215505349621022721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.147 Γ— 10⁹⁷(98-digit number)
21476018414784803899…64431010699242045441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,984,378 XPMΒ·at block #6,842,494 Β· updates every 60s
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