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Block #2,646,961

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 3:31:15 PM Β· Difficulty 11.7562 Β· 4,195,957 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
44720b61dbc2629417a4c8f1f5caa557b4f296c3f3b7b120ebd3577fb6bc7a9c
View on Chainz β†—

Height

#2,646,961

Difficulty

11.756194

Transactions

1

Size

201 B

Version

2

Bits

0bc195e8

Nonce

573,081,203

Timestamp

5/3/2018, 3:31:15 PM

Confirmations

4,195,957

Mined by

⛏️ P2SHANzz9Rwx9mapcj61CpzFqtP9N6234SRLXg

Merkle Root

7eebb50803912276d4b63573275d63ceb609d4e098e1972880abc674af26be51
Transactions (1)
Coinbase7eebb508039122…abc674af26be51
1 in β†’ 1 out7.2200 XPM110 B
ANzz9Rwx…234SRLXg
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.

7.794 Γ— 10⁹⁡(96-digit number)
77948710525481948860…39658928097068134401
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
7.794 Γ— 10⁹⁡(96-digit number)
77948710525481948860…39658928097068134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.558 Γ— 10⁹⁢(97-digit number)
15589742105096389772…79317856194136268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.117 Γ— 10⁹⁢(97-digit number)
31179484210192779544…58635712388272537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.235 Γ— 10⁹⁢(97-digit number)
62358968420385559088…17271424776545075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.247 Γ— 10⁹⁷(98-digit number)
12471793684077111817…34542849553090150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.494 Γ— 10⁹⁷(98-digit number)
24943587368154223635…69085699106180300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.988 Γ— 10⁹⁷(98-digit number)
49887174736308447270…38171398212360601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.977 Γ— 10⁹⁷(98-digit number)
99774349472616894541…76342796424721203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.995 Γ— 10⁹⁸(99-digit number)
19954869894523378908…52685592849442406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.990 Γ— 10⁹⁸(99-digit number)
39909739789046757816…05371185698884812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.981 Γ— 10⁹⁸(99-digit number)
79819479578093515632…10742371397769625601
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:57,987,691 XPMΒ·at block #6,842,917 Β· updates every 60s
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