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Block #2,720,617

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/25/2018, 10:28:06 AM Β· Difficulty 11.6137 Β· 4,122,780 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
24f9f2cf9cec81503ff1d793cd74dc03cab765689e5e9da6c80885eb3cce54b9
View on Chainz β†—

Height

#2,720,617

Difficulty

11.613652

Transactions

1

Size

200 B

Version

2

Bits

0b9d1844

Nonce

590,097,848

Timestamp

6/25/2018, 10:28:06 AM

Confirmations

4,122,780

Mined by

⛏️ P2SHARXww1rdAorWNHxafeRyfQXqvoaZpZQ3xS

Merkle Root

bdf08f7f0b9e00865f378ae7eb7a9af23cb170cb561d45a9041a6147016effa5
Transactions (1)
Coinbasebdf08f7f0b9e00…1a6147016effa5
1 in β†’ 1 out7.4000 XPM110 B
ARXww1rd…aZpZQ3xS
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.

1.378 Γ— 10⁹⁡(96-digit number)
13780639460790113829…70170693017437822721
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
1.378 Γ— 10⁹⁡(96-digit number)
13780639460790113829…70170693017437822721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.756 Γ— 10⁹⁡(96-digit number)
27561278921580227659…40341386034875645441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.512 Γ— 10⁹⁡(96-digit number)
55122557843160455318…80682772069751290881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.102 Γ— 10⁹⁢(97-digit number)
11024511568632091063…61365544139502581761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.204 Γ— 10⁹⁢(97-digit number)
22049023137264182127…22731088279005163521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.409 Γ— 10⁹⁢(97-digit number)
44098046274528364254…45462176558010327041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.819 Γ— 10⁹⁢(97-digit number)
88196092549056728509…90924353116020654081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.763 Γ— 10⁹⁷(98-digit number)
17639218509811345701…81848706232041308161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.527 Γ— 10⁹⁷(98-digit number)
35278437019622691403…63697412464082616321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.055 Γ— 10⁹⁷(98-digit number)
70556874039245382807…27394824928165232641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.411 Γ— 10⁹⁸(99-digit number)
14111374807849076561…54789649856330465281
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:57,991,540 XPMΒ·at block #6,843,396 Β· updates every 60s
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