Block #237,748

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/1/2013, 5:17:08 AM · Difficulty 9.9504 · 6,578,498 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
239c1f73aff4add233e747d173feff86cceed04d451ae9743ac3f2f512ffbe47

Height

#237,748

Difficulty

9.950406

Transactions

4

Size

1.29 KB

Version

2

Bits

09f34dc8

Nonce

1,214

Timestamp

11/1/2013, 5:17:08 AM

Confirmations

6,578,498

Merkle Root

5b1c874530170286ec9af29ae71cd661a1088a254a63321c217c8242356ef51b
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.

9.841 × 10⁹¹(92-digit number)
98411597944821607998…49077687939212026979
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
9.841 × 10⁹¹(92-digit number)
98411597944821607998…49077687939212026979
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.968 × 10⁹²(93-digit number)
19682319588964321599…98155375878424053959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.936 × 10⁹²(93-digit number)
39364639177928643199…96310751756848107919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.872 × 10⁹²(93-digit number)
78729278355857286398…92621503513696215839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.574 × 10⁹³(94-digit number)
15745855671171457279…85243007027392431679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.149 × 10⁹³(94-digit number)
31491711342342914559…70486014054784863359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.298 × 10⁹³(94-digit number)
62983422684685829119…40972028109569726719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.259 × 10⁹⁴(95-digit number)
12596684536937165823…81944056219139453439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.519 × 10⁹⁴(95-digit number)
25193369073874331647…63888112438278906879
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:57,774,087 XPM·at block #6,816,245 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy