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Block #164,568

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 6:17:21 PM Β· Difficulty 9.8628 Β· 6,649,527 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab9b635638da16ceb8fb2e985bd261b3ec453b1dcc8ecac6e3de97c9c5a9c1eb
View on Chainz β†—

Height

#164,568

Difficulty

9.862849

Transactions

1

Size

197 B

Version

2

Bits

09dce3ae

Nonce

109,631

Timestamp

9/14/2013, 6:17:21 PM

Confirmations

6,649,527

Mined by

⛏️ P2SHARdDiuG8TYpd2wtV15aZGy5J6Lwggxf9Qh

Merkle Root

547c8377a67c8a2cc68e4ff8d376fa3670f47ffa7f4a65215bb690f6ecefa7f4
Transactions (1)
Coinbase547c8377a67c8a…b690f6ecefa7f4
1 in β†’ 1 out10.2600 XPM109 B
ARdDiuG8…wggxf9Qh
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.

8.447 Γ— 10⁹⁰(91-digit number)
84476415562089677659…62178631249343248119
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
8.447 Γ— 10⁹⁰(91-digit number)
84476415562089677659…62178631249343248119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.689 Γ— 10⁹¹(92-digit number)
16895283112417935531…24357262498686496239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.379 Γ— 10⁹¹(92-digit number)
33790566224835871063…48714524997372992479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.758 Γ— 10⁹¹(92-digit number)
67581132449671742127…97429049994745984959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.351 Γ— 10⁹²(93-digit number)
13516226489934348425…94858099989491969919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.703 Γ— 10⁹²(93-digit number)
27032452979868696851…89716199978983939839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.406 Γ— 10⁹²(93-digit number)
54064905959737393702…79432399957967879679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.081 Γ— 10⁹³(94-digit number)
10812981191947478740…58864799915935759359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.162 Γ— 10⁹³(94-digit number)
21625962383894957480…17729599831871518719
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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