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Block #2,672,320

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/22/2018, 1:35:25 AM Β· Difficulty 11.6937 Β· 4,167,946 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6bdb9d87230cdcf7f1fe6cd368380ec1c0d88cda545b7bc84edfab8d033bf2ef
View on Chainz β†—

Height

#2,672,320

Difficulty

11.693701

Transactions

1

Size

201 B

Version

2

Bits

0bb1965e

Nonce

1,639,276,687

Timestamp

5/22/2018, 1:35:25 AM

Confirmations

4,167,946

Mined by

⛏️ P2SHAGX2qowyM8UFyd9ixMFqBjX5C5ry8UfVKp

Merkle Root

aa879a0cf207ea1c0b09fff525825450a6daa9f668d2e8ba2a89024597384d57
Transactions (1)
Coinbaseaa879a0cf207ea…89024597384d57
1 in β†’ 1 out7.3000 XPM110 B
AGX2qowy…ry8UfVKp
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.

1.096 Γ— 10⁹⁷(98-digit number)
10969225969159648564…96669055563032514561
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
1.096 Γ— 10⁹⁷(98-digit number)
10969225969159648564…96669055563032514561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.193 Γ— 10⁹⁷(98-digit number)
21938451938319297129…93338111126065029121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.387 Γ— 10⁹⁷(98-digit number)
43876903876638594259…86676222252130058241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.775 Γ— 10⁹⁷(98-digit number)
87753807753277188519…73352444504260116481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.755 Γ— 10⁹⁸(99-digit number)
17550761550655437703…46704889008520232961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.510 Γ— 10⁹⁸(99-digit number)
35101523101310875407…93409778017040465921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.020 Γ— 10⁹⁸(99-digit number)
70203046202621750815…86819556034080931841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.404 Γ— 10⁹⁹(100-digit number)
14040609240524350163…73639112068161863681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.808 Γ— 10⁹⁹(100-digit number)
28081218481048700326…47278224136323727361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.616 Γ— 10⁹⁹(100-digit number)
56162436962097400652…94556448272647454721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.123 Γ— 10¹⁰⁰(101-digit number)
11232487392419480130…89112896545294909441
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:57,966,442 XPMΒ·at block #6,840,265 Β· updates every 60s
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