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Block #2,634,406

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 9:22:20 PM Β· Difficulty 11.2431 Β· 4,201,949 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
68069ef80e460584804f504cf06ee88fd3d27522fc5013e9500a0822e170d008
View on Chainz β†—

Height

#2,634,406

Difficulty

11.243082

Transactions

2

Size

573 B

Version

2

Bits

0b3e3aa2

Nonce

1,118,263,576

Timestamp

4/28/2018, 9:22:20 PM

Confirmations

4,201,949

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

d2dbec0ffe9be539a9fdff9d2e3f2642f479dfd64a7d6a40fe28ef8baa7872e5
Transactions (2)
Coinbase87cdf841984a61…745796dd2220a6
1 in β†’ 1 out7.9100 XPM110 B
Adqah8zh…1WwoHJ9t
4c5def1360b871…6a62596321069d
2 in β†’ 2 out286.9021 XPM373 B
AGafMD9U…qUye8cWTAKhjCK4x…p7jQxgaQ
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.

2.305 Γ— 10⁹⁡(96-digit number)
23058486648475259853…18227696944756369921
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
2.305 Γ— 10⁹⁡(96-digit number)
23058486648475259853…18227696944756369921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.611 Γ— 10⁹⁡(96-digit number)
46116973296950519706…36455393889512739841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.223 Γ— 10⁹⁡(96-digit number)
92233946593901039412…72910787779025479681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.844 Γ— 10⁹⁢(97-digit number)
18446789318780207882…45821575558050959361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.689 Γ— 10⁹⁢(97-digit number)
36893578637560415765…91643151116101918721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.378 Γ— 10⁹⁢(97-digit number)
73787157275120831530…83286302232203837441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.475 Γ— 10⁹⁷(98-digit number)
14757431455024166306…66572604464407674881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.951 Γ— 10⁹⁷(98-digit number)
29514862910048332612…33145208928815349761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.902 Γ— 10⁹⁷(98-digit number)
59029725820096665224…66290417857630699521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.180 Γ— 10⁹⁸(99-digit number)
11805945164019333044…32580835715261399041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.361 Γ— 10⁹⁸(99-digit number)
23611890328038666089…65161671430522798081
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:57,935,100 XPMΒ·at block #6,836,354 Β· updates every 60s
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