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Block #1,624,232

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/11/2016, 9:33:18 PM Β· Difficulty 10.5883 Β· 5,186,755 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6a8c4048f92366a76a2c9bd5568fe65a1c276ea4e264c97c0e71b82dc53fd43a
View on Chainz β†—

Height

#1,624,232

Difficulty

10.588258

Transactions

2

Size

4.31 KB

Version

2

Bits

0a96981a

Nonce

890,219,289

Timestamp

6/11/2016, 9:33:18 PM

Confirmations

5,186,755

Mined by

⛏️ P2SHAY6hoiEscfjwYBYZtmK4EoARobNAEjQUeh

Merkle Root

ad83c761b6824fbac0198c98be04f1beec379dd5184fb813ef015d8e28910b9a
Transactions (2)
Coinbase36fc15d9f77a79…a6b627c8f2e075
1 in β†’ 1 out8.9600 XPM109 B
AY6hoiEs…NAEjQUeh
79fd4c95d90ff9…c57beb1a557252
28 in β†’ 2 out1.1206 XPM4.12 KB
AUMU9B8q…GQcV7HUTAe3ouoyv…gJ7YG3xv
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.

4.756 Γ— 10⁹⁴(95-digit number)
47569245713106688271…74694674011856089601
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
4.756 Γ— 10⁹⁴(95-digit number)
47569245713106688271…74694674011856089601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.513 Γ— 10⁹⁴(95-digit number)
95138491426213376543…49389348023712179201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.902 Γ— 10⁹⁡(96-digit number)
19027698285242675308…98778696047424358401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.805 Γ— 10⁹⁡(96-digit number)
38055396570485350617…97557392094848716801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.611 Γ— 10⁹⁡(96-digit number)
76110793140970701234…95114784189697433601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.522 Γ— 10⁹⁢(97-digit number)
15222158628194140246…90229568379394867201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.044 Γ— 10⁹⁢(97-digit number)
30444317256388280493…80459136758789734401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.088 Γ— 10⁹⁢(97-digit number)
60888634512776560987…60918273517579468801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.217 Γ— 10⁹⁷(98-digit number)
12177726902555312197…21836547035158937601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.435 Γ— 10⁹⁷(98-digit number)
24355453805110624395…43673094070317875201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.871 Γ— 10⁹⁷(98-digit number)
48710907610221248790…87346188140635750401
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:57,731,999 XPMΒ·at block #6,810,986 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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