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Block #1,112,458

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/17/2015, 7:39:14 AM Β· Difficulty 10.8958 Β· 5,701,604 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
97487c6077ba71553fd15e0f12296c86f24c67bebe8f67e1ebf1b9764385216f
View on Chainz β†—

Height

#1,112,458

Difficulty

10.895778

Transactions

2

Size

697 B

Version

2

Bits

0ae551b8

Nonce

2,078,048,546

Timestamp

6/17/2015, 7:39:14 AM

Confirmations

5,701,604

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

02f2ab8285669027f8a1ca52f207177e7548709e66771ae1e91f238d75652657
Transactions (2)
Coinbase72c58d3a0f8d65…b0663f3fd0965e
1 in β†’ 1 out8.4200 XPM116 B
AJCEY9yy…tg97E6zm
611c3074acbbb6…61db051083caf8
3 in β†’ 1 out446211.9800 XPM490 B
AMb2RL9J…zTbGj3be
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.

2.207 Γ— 10⁹⁢(97-digit number)
22077188940845714888…89266002603069091201
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
2.207 Γ— 10⁹⁢(97-digit number)
22077188940845714888…89266002603069091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.415 Γ— 10⁹⁢(97-digit number)
44154377881691429777…78532005206138182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.830 Γ— 10⁹⁢(97-digit number)
88308755763382859554…57064010412276364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.766 Γ— 10⁹⁷(98-digit number)
17661751152676571910…14128020824552729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.532 Γ— 10⁹⁷(98-digit number)
35323502305353143821…28256041649105459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.064 Γ— 10⁹⁷(98-digit number)
70647004610706287643…56512083298210918401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.412 Γ— 10⁹⁸(99-digit number)
14129400922141257528…13024166596421836801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.825 Γ— 10⁹⁸(99-digit number)
28258801844282515057…26048333192843673601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.651 Γ— 10⁹⁸(99-digit number)
56517603688565030114…52096666385687347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.130 Γ— 10⁹⁹(100-digit number)
11303520737713006022…04193332771374694401
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:57,756,573 XPMΒ·at block #6,814,061 Β· updates every 60s
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