Block #370,504

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2014, 4:50:33 AM · Difficulty 10.4381 · 6,440,192 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b60ab23ed3036e93e58d4895b04684cad09f87b26ce57938261d344617c0770

Height

#370,504

Difficulty

10.438068

Transactions

3

Size

673 B

Version

2

Bits

0a702536

Nonce

251,601

Timestamp

1/22/2014, 4:50:33 AM

Confirmations

6,440,192

Merkle Root

92a218c3023df34be19ddae966f2271a0bd95e62bc946b0a16c24bf39ec76dc5
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.

3.247 × 10⁹⁵(96-digit number)
32470403585321439954…31643665235577277721
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
3.247 × 10⁹⁵(96-digit number)
32470403585321439954…31643665235577277721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.494 × 10⁹⁵(96-digit number)
64940807170642879908…63287330471154555441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.298 × 10⁹⁶(97-digit number)
12988161434128575981…26574660942309110881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.597 × 10⁹⁶(97-digit number)
25976322868257151963…53149321884618221761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.195 × 10⁹⁶(97-digit number)
51952645736514303926…06298643769236443521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.039 × 10⁹⁷(98-digit number)
10390529147302860785…12597287538472887041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.078 × 10⁹⁷(98-digit number)
20781058294605721570…25194575076945774081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.156 × 10⁹⁷(98-digit number)
41562116589211443141…50389150153891548161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.312 × 10⁹⁷(98-digit number)
83124233178422886282…00778300307783096321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.662 × 10⁹⁸(99-digit number)
16624846635684577256…01556600615566192641
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,729,660 XPM·at block #6,810,695 · 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.

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