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Block #1,407,192

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/10/2016, 10:34:44 AM Β· Difficulty 10.8060 Β· 5,435,677 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6eb7f1798c071de368615d96d2d6911ea035fb89b20de0c2693ea5e441600fec
View on Chainz β†—

Height

#1,407,192

Difficulty

10.805967

Transactions

2

Size

424 B

Version

2

Bits

0ace53d6

Nonce

1,284,017,611

Timestamp

1/10/2016, 10:34:44 AM

Confirmations

5,435,677

Mined by

⛏️ P2SHAJFhszb2uqyV52jZd9ypJJVKiSijT2AmzP

Merkle Root

7446a5b4c173d34722cf92385638fd468167a3f7a8ba6b90b87a4e3170b2e53e
Transactions (2)
Coinbase260625d34fcc88…7ea2c8bb54d89f
1 in β†’ 1 out8.5600 XPM109 B
AJFhszb2…ijT2AmzP
76917c6ae0b32e…d50fa024998d2e
1 in β†’ 2 out148877.9637 XPM225 B
AUWrzULS…Avwh7EE5AQz5cxT1…6bpmEdXY
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.

4.190 Γ— 10⁹⁴(95-digit number)
41901737010706533654…57827148421990061481
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
4.190 Γ— 10⁹⁴(95-digit number)
41901737010706533654…57827148421990061481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.380 Γ— 10⁹⁴(95-digit number)
83803474021413067308…15654296843980122961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.676 Γ— 10⁹⁡(96-digit number)
16760694804282613461…31308593687960245921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.352 Γ— 10⁹⁡(96-digit number)
33521389608565226923…62617187375920491841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.704 Γ— 10⁹⁡(96-digit number)
67042779217130453846…25234374751840983681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.340 Γ— 10⁹⁢(97-digit number)
13408555843426090769…50468749503681967361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.681 Γ— 10⁹⁢(97-digit number)
26817111686852181538…00937499007363934721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.363 Γ— 10⁹⁢(97-digit number)
53634223373704363077…01874998014727869441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.072 Γ— 10⁹⁷(98-digit number)
10726844674740872615…03749996029455738881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.145 Γ— 10⁹⁷(98-digit number)
21453689349481745230…07499992058911477761
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:57,987,295 XPMΒ·at block #6,842,868 Β· updates every 60s
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