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Block #77,499

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/22/2013, 10:47:11 AM Β· Difficulty 9.1760 Β· 6,732,125 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
172b35330e159162687a2898e63e03237100c49937627e1059018010aa904fc7
View on Chainz β†—

Height

#77,499

Difficulty

9.176033

Transactions

1

Size

197 B

Version

2

Bits

092d107e

Nonce

371

Timestamp

7/22/2013, 10:47:11 AM

Confirmations

6,732,125

Mined by

⛏️ P2SHAaECuzm1KMfZFVh6YTfPuB4vaZCgaQsWLR

Merkle Root

c35bd8aa1c47526b0463dcc7917a4019cc46242a6cfc4bccb5547a900bd6e4a1
Transactions (1)
Coinbasec35bd8aa1c4752…547a900bd6e4a1
1 in β†’ 1 out11.8600 XPM110 B
AaECuzm1…CgaQsWLR
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.

7.135 Γ— 10⁸⁢(87-digit number)
71357027151625339092…17644532956049017139
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
7.135 Γ— 10⁸⁢(87-digit number)
71357027151625339092…17644532956049017139
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.427 Γ— 10⁸⁷(88-digit number)
14271405430325067818…35289065912098034279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.854 Γ— 10⁸⁷(88-digit number)
28542810860650135637…70578131824196068559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.708 Γ— 10⁸⁷(88-digit number)
57085621721300271274…41156263648392137119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.141 Γ— 10⁸⁸(89-digit number)
11417124344260054254…82312527296784274239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.283 Γ— 10⁸⁸(89-digit number)
22834248688520108509…64625054593568548479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.566 Γ— 10⁸⁸(89-digit number)
45668497377040217019…29250109187137096959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.133 Γ— 10⁸⁸(89-digit number)
91336994754080434038…58500218374274193919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.826 Γ— 10⁸⁹(90-digit number)
18267398950816086807…17000436748548387839
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
Circulating Supply:57,721,069 XPMΒ·at block #6,809,623 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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