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Block #2,815,273

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2018, 12:13:44 PM Β· Difficulty 11.6831 Β· 4,021,714 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e9f64a489189b338960dbef4a9239ca1c8edc96032cb691d56d4e93b912a9b34
View on Chainz β†—

Height

#2,815,273

Difficulty

11.683060

Transactions

1

Size

200 B

Version

2

Bits

0baedd05

Nonce

247,498,313

Timestamp

8/29/2018, 12:13:44 PM

Confirmations

4,021,714

Mined by

⛏️ P2SHAZemPr8nLafqKxmmW1uNDot88vHCsAk1qy

Merkle Root

0b88e1ad576eb7ee1d8ffc08663faca3639d34b2fcea4dd2f7a45061408219a9
Transactions (1)
Coinbase0b88e1ad576eb7…a45061408219a9
1 in β†’ 1 out7.3100 XPM110 B
AZemPr8n…HCsAk1qy
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.

7.515 Γ— 10⁹³(94-digit number)
75154468777606602942…08721411717988763361
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
7.515 Γ— 10⁹³(94-digit number)
75154468777606602942…08721411717988763361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.503 Γ— 10⁹⁴(95-digit number)
15030893755521320588…17442823435977526721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.006 Γ— 10⁹⁴(95-digit number)
30061787511042641176…34885646871955053441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.012 Γ— 10⁹⁴(95-digit number)
60123575022085282353…69771293743910106881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.202 Γ— 10⁹⁡(96-digit number)
12024715004417056470…39542587487820213761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.404 Γ— 10⁹⁡(96-digit number)
24049430008834112941…79085174975640427521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.809 Γ— 10⁹⁡(96-digit number)
48098860017668225882…58170349951280855041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.619 Γ— 10⁹⁡(96-digit number)
96197720035336451765…16340699902561710081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.923 Γ— 10⁹⁢(97-digit number)
19239544007067290353…32681399805123420161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.847 Γ— 10⁹⁢(97-digit number)
38479088014134580706…65362799610246840321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.695 Γ— 10⁹⁢(97-digit number)
76958176028269161412…30725599220493680641
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:57,940,196 XPMΒ·at block #6,836,986 Β· updates every 60s
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