Block #62,328

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2013, 6:32:30 PM · Difficulty 8.9761 · 6,740,443 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
61fda55ff05d39bee622b5f2cc02c1649b0c919d06861749376aa09cc23e5e17

Height

#62,328

Difficulty

8.976055

Transactions

5

Size

1.08 KB

Version

2

Bits

08f9dec0

Nonce

380

Timestamp

7/18/2013, 6:32:30 PM

Confirmations

6,740,443

Merkle Root

f16bc074f8e86457aa44be86000902483d66aee5eadb6236ae46698b370c2837
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.930 × 10¹¹²(113-digit number)
49306251430323034405…41149847198858406609
Discovered Prime Numbers
p_k = 2^k × origin − 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 − 1
4.930 × 10¹¹²(113-digit number)
49306251430323034405…41149847198858406609
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.861 × 10¹¹²(113-digit number)
98612502860646068810…82299694397716813219
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.972 × 10¹¹³(114-digit number)
19722500572129213762…64599388795433626439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.944 × 10¹¹³(114-digit number)
39445001144258427524…29198777590867252879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.889 × 10¹¹³(114-digit number)
78890002288516855048…58397555181734505759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.577 × 10¹¹⁴(115-digit number)
15778000457703371009…16795110363469011519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.155 × 10¹¹⁴(115-digit number)
31556000915406742019…33590220726938023039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.311 × 10¹¹⁴(115-digit number)
63112001830813484038…67180441453876046079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.262 × 10¹¹⁵(116-digit number)
12622400366162696807…34360882907752092159
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,666,193 XPM·at block #6,802,770 · updates every 60s
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