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Block #197,921

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/7/2013, 10:18:45 AM Β· Difficulty 9.8843 Β· 6,626,626 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
091c17aab6873e5fdcb7e19044c07e6231aacd8c0c434ddf07573b304fcf6c6a
View on Chainz β†—

Height

#197,921

Difficulty

9.884299

Transactions

1

Size

198 B

Version

2

Bits

09e2616a

Nonce

286,542

Timestamp

10/7/2013, 10:18:45 AM

Confirmations

6,626,626

Mined by

⛏️ P2SHAHNdTz9RdyhMpsaRttP7HwiXvgDHU2jpcA

Merkle Root

ba686f7cdd48d786ffe4d503092df442b7b42396028fc94ee58f7c9d66eba168
Transactions (1)
Coinbaseba686f7cdd48d7…8f7c9d66eba168
1 in β†’ 1 out10.2200 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.

2.637 Γ— 10⁹¹(92-digit number)
26378650197057551405…45689524041531529119
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
2.637 Γ— 10⁹¹(92-digit number)
26378650197057551405…45689524041531529119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.275 Γ— 10⁹¹(92-digit number)
52757300394115102811…91379048083063058239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.055 Γ— 10⁹²(93-digit number)
10551460078823020562…82758096166126116479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.110 Γ— 10⁹²(93-digit number)
21102920157646041124…65516192332252232959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.220 Γ— 10⁹²(93-digit number)
42205840315292082249…31032384664504465919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.441 Γ— 10⁹²(93-digit number)
84411680630584164499…62064769329008931839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.688 Γ— 10⁹³(94-digit number)
16882336126116832899…24129538658017863679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.376 Γ— 10⁹³(94-digit number)
33764672252233665799…48259077316035727359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.752 Γ— 10⁹³(94-digit number)
67529344504467331599…96518154632071454719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
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