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Block #2,335,779

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/13/2017, 10:46:21 PM Β· Difficulty 10.9204 Β· 4,476,914 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eff6a98cd5a99f22b0a587642256332dbef6e87ded883aa928b9e2b88403519e
View on Chainz β†—

Height

#2,335,779

Difficulty

10.920364

Transactions

2

Size

723 B

Version

2

Bits

0aeb9cf2

Nonce

227,652,594

Timestamp

10/13/2017, 10:46:21 PM

Confirmations

4,476,914

Mined by

⛏️ P2SHANpiZVywYp6oZH8FkWxJBGo4JpG2K4sFJ7

Merkle Root

813055b7aee8615d3b7232fa208468c3b9a9a4a09e8d32ba8ccc69353255c481
Transactions (2)
Coinbase65deba2b6564bf…c56f004a8f9d30
1 in β†’ 1 out8.3800 XPM110 B
ANpiZVyw…G2K4sFJ7
302d58cd764ea9…ba035f85b98491
3 in β†’ 2 out129.6750 XPM523 B
AQTpuy3q…iwZmhK8pAe4scM3b…87aFGpfp
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.

1.352 Γ— 10⁹⁡(96-digit number)
13521396284657762313…30319234107070972801
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
1.352 Γ— 10⁹⁡(96-digit number)
13521396284657762313…30319234107070972801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.704 Γ— 10⁹⁡(96-digit number)
27042792569315524626…60638468214141945601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.408 Γ— 10⁹⁡(96-digit number)
54085585138631049252…21276936428283891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.081 Γ— 10⁹⁢(97-digit number)
10817117027726209850…42553872856567782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.163 Γ— 10⁹⁢(97-digit number)
21634234055452419700…85107745713135564801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.326 Γ— 10⁹⁢(97-digit number)
43268468110904839401…70215491426271129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.653 Γ— 10⁹⁢(97-digit number)
86536936221809678803…40430982852542259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.730 Γ— 10⁹⁷(98-digit number)
17307387244361935760…80861965705084518401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.461 Γ— 10⁹⁷(98-digit number)
34614774488723871521…61723931410169036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.922 Γ— 10⁹⁷(98-digit number)
69229548977447743042…23447862820338073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.384 Γ— 10⁹⁸(99-digit number)
13845909795489548608…46895725640676147201
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:57,745,579 XPMΒ·at block #6,812,692 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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