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Block #2,634,724

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 12:07:29 AM Β· Difficulty 11.2656 Β· 4,196,933 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8b3c084f490ca72f74f124bb7b211de615d8f989ac05e33e612e4ce549df2ebb
View on Chainz β†—

Height

#2,634,724

Difficulty

11.265624

Transactions

2

Size

724 B

Version

2

Bits

0b43fff5

Nonce

39,712,462

Timestamp

4/29/2018, 12:07:29 AM

Confirmations

4,196,933

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

e6b9b96b47549e0b4827537a6bcc79b3c8520f607e993522d67484431e8bafbe
Transactions (2)
Coinbasef2737ec454a400…17c38e2f550941
1 in β†’ 1 out7.8800 XPM110 B
Adqah8zh…1WwoHJ9t
e2005735dbf28d…0cb1adaf98fadb
3 in β†’ 2 out4131.8929 XPM525 B
AW3AB4vs…i2UMoEEyARywRRZa…HVd3P31R
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.

8.955 Γ— 10⁹¹(92-digit number)
89554495421941170890…94183456084421742561
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
8.955 Γ— 10⁹¹(92-digit number)
89554495421941170890…94183456084421742561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.791 Γ— 10⁹²(93-digit number)
17910899084388234178…88366912168843485121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.582 Γ— 10⁹²(93-digit number)
35821798168776468356…76733824337686970241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.164 Γ— 10⁹²(93-digit number)
71643596337552936712…53467648675373940481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.432 Γ— 10⁹³(94-digit number)
14328719267510587342…06935297350747880961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.865 Γ— 10⁹³(94-digit number)
28657438535021174685…13870594701495761921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.731 Γ— 10⁹³(94-digit number)
57314877070042349370…27741189402991523841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.146 Γ— 10⁹⁴(95-digit number)
11462975414008469874…55482378805983047681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.292 Γ— 10⁹⁴(95-digit number)
22925950828016939748…10964757611966095361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.585 Γ— 10⁹⁴(95-digit number)
45851901656033879496…21929515223932190721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.170 Γ— 10⁹⁴(95-digit number)
91703803312067758992…43859030447864381441
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:57,897,362 XPMΒ·at block #6,831,656 Β· updates every 60s
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