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Block #1,421,424

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/20/2016, 4:14:20 PM Β· Difficulty 10.7859 Β· 5,415,569 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6dca7144b74b0e6678715442f11ad01f5617baf80fa1283e6148076ca5baf2cf
View on Chainz β†—

Height

#1,421,424

Difficulty

10.785941

Transactions

2

Size

2.47 KB

Version

2

Bits

0ac9336f

Nonce

326,953,078

Timestamp

1/20/2016, 4:14:20 PM

Confirmations

5,415,569

Mined by

⛏️ P2SHAPs55c3QLyKEd7QLhLtmTGk2JYYCDeYxUY

Merkle Root

56521a88d226945ada6e1cc318a3716a49f63e35acd302eb215ac50f01dc8cfd
Transactions (2)
Coinbase9911310c2e7fdc…8fd4e880b23ce8
1 in β†’ 1 out8.6100 XPM109 B
APs55c3Q…YCDeYxUY
c7da966c5e1384…ea4a8d66d721cb
15 in β†’ 3 out1987.2646 XPM2.28 KB
AULJqW7T…TL2PLdFsAZc14Jsm…a7rveLrZATJeka45…7yXJQkRn
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.

8.740 Γ— 10⁹³(94-digit number)
87400983414253121890…42939959865614986001
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
8.740 Γ— 10⁹³(94-digit number)
87400983414253121890…42939959865614986001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.748 Γ— 10⁹⁴(95-digit number)
17480196682850624378…85879919731229972001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.496 Γ— 10⁹⁴(95-digit number)
34960393365701248756…71759839462459944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.992 Γ— 10⁹⁴(95-digit number)
69920786731402497512…43519678924919888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.398 Γ— 10⁹⁡(96-digit number)
13984157346280499502…87039357849839776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.796 Γ— 10⁹⁡(96-digit number)
27968314692560999004…74078715699679552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.593 Γ— 10⁹⁡(96-digit number)
55936629385121998009…48157431399359104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.118 Γ— 10⁹⁢(97-digit number)
11187325877024399601…96314862798718208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.237 Γ— 10⁹⁢(97-digit number)
22374651754048799203…92629725597436416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.474 Γ— 10⁹⁢(97-digit number)
44749303508097598407…85259451194872832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.949 Γ— 10⁹⁢(97-digit number)
89498607016195196815…70518902389745664001
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:57,940,245 XPMΒ·at block #6,836,992 Β· updates every 60s
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