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Block #2,089,478

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/27/2017, 1:36:35 AM Β· Difficulty 10.8756 Β· 4,737,827 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c54a04df69fa6618a9e734885f7fe70e9c4452ec40e85f6278a5808100af37d1
View on Chainz β†—

Height

#2,089,478

Difficulty

10.875644

Transactions

2

Size

1.72 KB

Version

2

Bits

0ae02a31

Nonce

491,691,281

Timestamp

4/27/2017, 1:36:35 AM

Confirmations

4,737,827

Mined by

⛏️ P2SHAGhd7WwkoxboSaMsT4KxoDNKS3wa3iEAeK

Merkle Root

e5e9d742deaee0a713d30ac06f2214d0c3a2c77efc7e0abb8c05e345f030d78d
Transactions (2)
Coinbase04daed2e9ea263…058c23db1337ae
1 in β†’ 1 out8.4600 XPM109 B
AGhd7Wwk…wa3iEAeK
d68f989a87ff73…2727b04db31ac1
10 in β†’ 2 out1245.5560 XPM1.52 KB
ANNmHVZ5…chFkeLK2AQb2bLW5…xLaKJDK9
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.

8.334 Γ— 10⁹⁡(96-digit number)
83342470242506709506…05920892564055992321
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
8.334 Γ— 10⁹⁡(96-digit number)
83342470242506709506…05920892564055992321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.666 Γ— 10⁹⁢(97-digit number)
16668494048501341901…11841785128111984641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.333 Γ— 10⁹⁢(97-digit number)
33336988097002683802…23683570256223969281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.667 Γ— 10⁹⁢(97-digit number)
66673976194005367604…47367140512447938561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.333 Γ— 10⁹⁷(98-digit number)
13334795238801073520…94734281024895877121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.666 Γ— 10⁹⁷(98-digit number)
26669590477602147041…89468562049791754241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.333 Γ— 10⁹⁷(98-digit number)
53339180955204294083…78937124099583508481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.066 Γ— 10⁹⁸(99-digit number)
10667836191040858816…57874248199167016961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.133 Γ— 10⁹⁸(99-digit number)
21335672382081717633…15748496398334033921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.267 Γ— 10⁹⁸(99-digit number)
42671344764163435267…31496992796668067841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.534 Γ— 10⁹⁸(99-digit number)
85342689528326870534…62993985593336135681
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:57,862,551 XPMΒ·at block #6,827,304 Β· updates every 60s
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