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Block #1,615,814

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/6/2016, 1:44:32 AM Β· Difficulty 10.5858 Β· 5,200,883 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
01d6af35c55817af1e4a19e3ecd1c35f798ed5253176264ce8209f8768dd9b17
View on Chainz β†—

Height

#1,615,814

Difficulty

10.585791

Transactions

2

Size

8.07 KB

Version

2

Bits

0a95f662

Nonce

1,367,304,175

Timestamp

6/6/2016, 1:44:32 AM

Confirmations

5,200,883

Mined by

⛏️ P2SHAJY9hQu2wSPNCmuh6yBkGSjLGE85yBbXdz

Merkle Root

7bc7a7438e05c47b92252fcd943174d2679ede1909ea6397dbf7fd469681533e
Transactions (2)
Coinbaseb480b92e3e10be…51a5e99dc7ed93
1 in β†’ 1 out9.0100 XPM110 B
AJY9hQu2…85yBbXdz
af03fe9a68766a…e636516353f63d
54 in β†’ 2 out98.9100 XPM7.88 KB
AZ842mqM…uoA6Cef6ASx6PQvt…fWqRrJag
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.

7.170 Γ— 10⁹³(94-digit number)
71707680796176206064…33683858826678279901
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
7.170 Γ— 10⁹³(94-digit number)
71707680796176206064…33683858826678279901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.434 Γ— 10⁹⁴(95-digit number)
14341536159235241212…67367717653356559801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.868 Γ— 10⁹⁴(95-digit number)
28683072318470482425…34735435306713119601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.736 Γ— 10⁹⁴(95-digit number)
57366144636940964851…69470870613426239201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.147 Γ— 10⁹⁡(96-digit number)
11473228927388192970…38941741226852478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.294 Γ— 10⁹⁡(96-digit number)
22946457854776385940…77883482453704956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.589 Γ— 10⁹⁡(96-digit number)
45892915709552771881…55766964907409913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.178 Γ— 10⁹⁡(96-digit number)
91785831419105543762…11533929814819827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.835 Γ— 10⁹⁢(97-digit number)
18357166283821108752…23067859629639654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.671 Γ— 10⁹⁢(97-digit number)
36714332567642217505…46135719259279308801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,777,698 XPMΒ·at block #6,816,696 Β· updates every 60s
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