Block #80,462

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/24/2013, 4:18:27 AM · Difficulty 9.2501 · 6,729,231 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
853ad9c421f58b8356a26dabb21e835b13f01ceaa3f07cb6c0fe2b14da0f1702

Height

#80,462

Difficulty

9.250083

Transactions

3

Size

556 B

Version

2

Bits

09400577

Nonce

66,060

Timestamp

7/24/2013, 4:18:27 AM

Confirmations

6,729,231

Merkle Root

69d7f1a293a4c4d0ed04349edb531a8de187070c0d7d56c97813c85eb2e14352
Transactions (3)
1 in → 1 out11.6900 XPM109 B
1 in → 1 out11.9100 XPM159 B
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.

1.043 × 10¹⁰⁹(110-digit number)
10437136644127157914…93041587875581161329
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
1.043 × 10¹⁰⁹(110-digit number)
10437136644127157914…93041587875581161329
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.087 × 10¹⁰⁹(110-digit number)
20874273288254315829…86083175751162322659
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.174 × 10¹⁰⁹(110-digit number)
41748546576508631659…72166351502324645319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.349 × 10¹⁰⁹(110-digit number)
83497093153017263319…44332703004649290639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.669 × 10¹¹⁰(111-digit number)
16699418630603452663…88665406009298581279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.339 × 10¹¹⁰(111-digit number)
33398837261206905327…77330812018597162559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.679 × 10¹¹⁰(111-digit number)
66797674522413810655…54661624037194325119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.335 × 10¹¹¹(112-digit number)
13359534904482762131…09323248074388650239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.671 × 10¹¹¹(112-digit number)
26719069808965524262…18646496148777300479
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:57,721,621 XPM·at block #6,809,692 · updates every 60s
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