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Block #2,132,877

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2017, 2:50:30 AM Β· Difficulty 10.9100 Β· 4,709,336 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
67b5800fae482f88affc3c77d5f3ab8cfbe9c111182cd4828beae06cd063cc3e
View on Chainz β†—

Height

#2,132,877

Difficulty

10.910013

Transactions

1

Size

200 B

Version

2

Bits

0ae8f6a3

Nonce

210,223,025

Timestamp

5/26/2017, 2:50:30 AM

Confirmations

4,709,336

Mined by

⛏️ P2SHATHYvsTZQsZtQSvYPJsLEbV1gdvzU9FrqC

Merkle Root

6d8349811e3478af4d03c23c494ccb0385095cac198431e6a8ffd3368dde376f
Transactions (1)
Coinbase6d8349811e3478…ffd3368dde376f
1 in β†’ 1 out8.3900 XPM109 B
ATHYvsTZ…vzU9FrqC
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.

1.284 Γ— 10⁹⁷(98-digit number)
12842314830260902943…56769545667741532161
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
1.284 Γ— 10⁹⁷(98-digit number)
12842314830260902943…56769545667741532161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.568 Γ— 10⁹⁷(98-digit number)
25684629660521805887…13539091335483064321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.136 Γ— 10⁹⁷(98-digit number)
51369259321043611775…27078182670966128641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.027 Γ— 10⁹⁸(99-digit number)
10273851864208722355…54156365341932257281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.054 Γ— 10⁹⁸(99-digit number)
20547703728417444710…08312730683864514561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.109 Γ— 10⁹⁸(99-digit number)
41095407456834889420…16625461367729029121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.219 Γ— 10⁹⁸(99-digit number)
82190814913669778840…33250922735458058241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.643 Γ— 10⁹⁹(100-digit number)
16438162982733955768…66501845470916116481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.287 Γ— 10⁹⁹(100-digit number)
32876325965467911536…33003690941832232961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.575 Γ— 10⁹⁹(100-digit number)
65752651930935823072…66007381883664465921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.315 Γ— 10¹⁰⁰(101-digit number)
13150530386187164614…32014763767328931841
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:57,982,101 XPMΒ·at block #6,842,212 Β· updates every 60s
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