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Block #195,728

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/6/2013, 12:25:44 AM Β· Difficulty 9.8803 Β· 6,619,410 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
84e1fc03fe43db5d693354b42e80a4247dca295f667700f2daaa8a9903a53598
View on Chainz β†—

Height

#195,728

Difficulty

9.880320

Transactions

1

Size

200 B

Version

2

Bits

09e15caa

Nonce

148,215

Timestamp

10/6/2013, 12:25:44 AM

Confirmations

6,619,410

Mined by

⛏️ P2SHAHNdTz9RdyhMpsaRttP7HwiXvgDHU2jpcA

Merkle Root

39dc3b3f3ff6f06e8f3fc6b30c86ad90ea6f378cfe7acf3c493bc58dc8352826
Transactions (1)
Coinbase39dc3b3f3ff6f0…3bc58dc8352826
1 in β†’ 1 out10.2300 XPM109 B
AHNdTz9R…DHU2jpcA
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.

3.592 Γ— 10⁹⁢(97-digit number)
35926858269007058534…15509046033803270399
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
3.592 Γ— 10⁹⁢(97-digit number)
35926858269007058534…15509046033803270399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.185 Γ— 10⁹⁢(97-digit number)
71853716538014117068…31018092067606540799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.437 Γ— 10⁹⁷(98-digit number)
14370743307602823413…62036184135213081599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.874 Γ— 10⁹⁷(98-digit number)
28741486615205646827…24072368270426163199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.748 Γ— 10⁹⁷(98-digit number)
57482973230411293655…48144736540852326399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.149 Γ— 10⁹⁸(99-digit number)
11496594646082258731…96289473081704652799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.299 Γ— 10⁹⁸(99-digit number)
22993189292164517462…92578946163409305599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.598 Γ— 10⁹⁸(99-digit number)
45986378584329034924…85157892326818611199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.197 Γ— 10⁹⁸(99-digit number)
91972757168658069848…70315784653637222399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.839 Γ— 10⁹⁹(100-digit number)
18394551433731613969…40631569307274444799
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:57,765,197 XPMΒ·at block #6,815,137 Β· updates every 60s
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