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Block #2,716,657

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/22/2018, 4:28:23 PM Β· Difficulty 11.6135 Β· 4,126,188 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1a35bb92ad9ffc4c936add80e440f4d8d1f00a34a127def219bc8c153d69b49
View on Chainz β†—

Height

#2,716,657

Difficulty

11.613463

Transactions

1

Size

200 B

Version

2

Bits

0b9d0bef

Nonce

482,275,396

Timestamp

6/22/2018, 4:28:23 PM

Confirmations

4,126,188

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

6887a8ad28657390123ee2aac83b8fccfadcf16d1ea4ec22b4520a2f138706cd
Transactions (1)
Coinbase6887a8ad286573…520a2f138706cd
1 in β†’ 1 out7.4000 XPM110 B
AZtxQr2F…7grUWrUz
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.

9.204 Γ— 10⁹⁴(95-digit number)
92042968659782006912…95647236852229946701
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
9.204 Γ— 10⁹⁴(95-digit number)
92042968659782006912…95647236852229946701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.840 Γ— 10⁹⁡(96-digit number)
18408593731956401382…91294473704459893401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.681 Γ— 10⁹⁡(96-digit number)
36817187463912802765…82588947408919786801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.363 Γ— 10⁹⁡(96-digit number)
73634374927825605530…65177894817839573601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.472 Γ— 10⁹⁢(97-digit number)
14726874985565121106…30355789635679147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.945 Γ— 10⁹⁢(97-digit number)
29453749971130242212…60711579271358294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.890 Γ— 10⁹⁢(97-digit number)
58907499942260484424…21423158542716588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.178 Γ— 10⁹⁷(98-digit number)
11781499988452096884…42846317085433177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.356 Γ— 10⁹⁷(98-digit number)
23562999976904193769…85692634170866355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.712 Γ— 10⁹⁷(98-digit number)
47125999953808387539…71385268341732710401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.425 Γ— 10⁹⁷(98-digit number)
94251999907616775078…42770536683465420801
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:57,987,105 XPMΒ·at block #6,842,844 Β· updates every 60s
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