Block #149,039

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/4/2013, 2:45:20 AM · Difficulty 9.8568 · 6,660,927 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
28ce8b269c1733e23c967f7feb4ee8a95300a3f059be23d08348d0ee9e13471f

Height

#149,039

Difficulty

9.856792

Transactions

4

Size

1.00 KB

Version

2

Bits

09db56c0

Nonce

282,925

Timestamp

9/4/2013, 2:45:20 AM

Confirmations

6,660,927

Merkle Root

dcd1ec9478f9028874ad68f9bbf92384d81fa10b7e70f9f309aee4af958011d2
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.

3.244 × 10⁹³(94-digit number)
32445138385707988235…96762158478773696099
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
3.244 × 10⁹³(94-digit number)
32445138385707988235…96762158478773696099
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.489 × 10⁹³(94-digit number)
64890276771415976470…93524316957547392199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.297 × 10⁹⁴(95-digit number)
12978055354283195294…87048633915094784399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.595 × 10⁹⁴(95-digit number)
25956110708566390588…74097267830189568799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.191 × 10⁹⁴(95-digit number)
51912221417132781176…48194535660379137599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.038 × 10⁹⁵(96-digit number)
10382444283426556235…96389071320758275199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.076 × 10⁹⁵(96-digit number)
20764888566853112470…92778142641516550399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.152 × 10⁹⁵(96-digit number)
41529777133706224941…85556285283033100799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.305 × 10⁹⁵(96-digit number)
83059554267412449882…71112570566066201599
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:57,723,800 XPM·at block #6,809,965 · updates every 60s
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