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Block #167,714

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/16/2013, 7:37:49 PM Β· Difficulty 9.8680 Β· 6,650,219 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1d435391547ff4e7093ec4659a143aecfa31c893cec889a5f044f87f660085d1
View on Chainz β†—

Height

#167,714

Difficulty

9.867992

Transactions

1

Size

203 B

Version

2

Bits

09de34b9

Nonce

33,556,208

Timestamp

9/16/2013, 7:37:49 PM

Confirmations

6,650,219

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

cfc3ea78b997265407eb5bfbed3f1922ba171a34a6ec98e09ef5c844bc5ed39f
Transactions (1)
Coinbasecfc3ea78b99726…f5c844bc5ed39f
1 in β†’ 1 out10.2500 XPM112 B
AcLBm5Z9…S683d7c3
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.

3.529 Γ— 10⁹⁢(97-digit number)
35290825306324647174…09917750865283977299
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.529 Γ— 10⁹⁢(97-digit number)
35290825306324647174…09917750865283977299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.058 Γ— 10⁹⁢(97-digit number)
70581650612649294349…19835501730567954599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.411 Γ— 10⁹⁷(98-digit number)
14116330122529858869…39671003461135909199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.823 Γ— 10⁹⁷(98-digit number)
28232660245059717739…79342006922271818399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.646 Γ— 10⁹⁷(98-digit number)
56465320490119435479…58684013844543636799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.129 Γ— 10⁹⁸(99-digit number)
11293064098023887095…17368027689087273599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.258 Γ— 10⁹⁸(99-digit number)
22586128196047774191…34736055378174547199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.517 Γ— 10⁹⁸(99-digit number)
45172256392095548383…69472110756349094399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.034 Γ— 10⁹⁸(99-digit number)
90344512784191096766…38944221512698188799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.806 Γ— 10⁹⁹(100-digit number)
18068902556838219353…77888443025396377599
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,787,529 XPMΒ·at block #6,817,932 Β· updates every 60s
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