Block #149,267

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/4/2013, 6:42:10 AM · Difficulty 9.8566 · 6,653,601 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
24f4d02080ae69d619226a29cb74ef4b9cea6d8774b536d0d4def9c1bf71407b

Height

#149,267

Difficulty

9.856646

Transactions

3

Size

945 B

Version

2

Bits

09db4d2e

Nonce

148,161

Timestamp

9/4/2013, 6:42:10 AM

Confirmations

6,653,601

Merkle Root

7fdabae52b408db823824609044f52b1665d15a72b80e12ed5c7d2adabfb4ede
Transactions (3)
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.

1.955 × 10⁹³(94-digit number)
19556951940990029526…19475161535590862079
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
1.955 × 10⁹³(94-digit number)
19556951940990029526…19475161535590862079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.911 × 10⁹³(94-digit number)
39113903881980059052…38950323071181724159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.822 × 10⁹³(94-digit number)
78227807763960118105…77900646142363448319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.564 × 10⁹⁴(95-digit number)
15645561552792023621…55801292284726896639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.129 × 10⁹⁴(95-digit number)
31291123105584047242…11602584569453793279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.258 × 10⁹⁴(95-digit number)
62582246211168094484…23205169138907586559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.251 × 10⁹⁵(96-digit number)
12516449242233618896…46410338277815173119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.503 × 10⁹⁵(96-digit number)
25032898484467237793…92820676555630346239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.006 × 10⁹⁵(96-digit number)
50065796968934475587…85641353111260692479
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:57,666,967 XPM·at block #6,802,867 · updates every 60s
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