Block #149,176

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/4/2013, 5:14:09 AM · Difficulty 9.8565 · 6,653,398 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b6f4b0fb3b1f013e9a390004d92bce1b295d4ea5c0711db73f7aa4450251ff60

Height

#149,176

Difficulty

9.856528

Transactions

3

Size

4.13 KB

Version

2

Bits

09db4567

Nonce

261,833

Timestamp

9/4/2013, 5:14:09 AM

Confirmations

6,653,398

Merkle Root

d8090de0eb42fda1cd5a01e18b7ac0faf615e05236470269139aec2611a33997
Transactions (3)
1 in → 1 out10.3300 XPM109 B
1 in → 1 out10.2900 XPM157 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.

7.539 × 10⁹¹(92-digit number)
75398163425657060176…61960388315496277959
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
7.539 × 10⁹¹(92-digit number)
75398163425657060176…61960388315496277959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.507 × 10⁹²(93-digit number)
15079632685131412035…23920776630992555919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.015 × 10⁹²(93-digit number)
30159265370262824070…47841553261985111839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.031 × 10⁹²(93-digit number)
60318530740525648141…95683106523970223679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.206 × 10⁹³(94-digit number)
12063706148105129628…91366213047940447359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.412 × 10⁹³(94-digit number)
24127412296210259256…82732426095880894719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.825 × 10⁹³(94-digit number)
48254824592420518513…65464852191761789439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.650 × 10⁹³(94-digit number)
96509649184841037026…30929704383523578879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.930 × 10⁹⁴(95-digit number)
19301929836968207405…61859408767047157759
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:57,664,608 XPM·at block #6,802,573 · updates every 60s
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