Block #1,229,795

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/10/2015, 4:45:03 AM · Difficulty 10.7365 · 5,560,231 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c1a0909fd14b64634d9328698cf06ddd4479a3b5df16654cfca1739de9966304

Height

#1,229,795

Difficulty

10.736491

Transactions

4

Size

1.29 KB

Version

2

Bits

0abc8aaa

Nonce

670,597,203

Timestamp

9/10/2015, 4:45:03 AM

Confirmations

5,560,231

Merkle Root

869bf8c4fe7d56aff5dc7b9a19c3fdd220a45bb9d4c76ebb31a61c1127dc283c
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.

9.178 × 10⁹²(93-digit number)
91785135538494811965…91481088784487544319
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
9.178 × 10⁹²(93-digit number)
91785135538494811965…91481088784487544319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.835 × 10⁹³(94-digit number)
18357027107698962393…82962177568975088639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.671 × 10⁹³(94-digit number)
36714054215397924786…65924355137950177279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.342 × 10⁹³(94-digit number)
73428108430795849572…31848710275900354559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.468 × 10⁹⁴(95-digit number)
14685621686159169914…63697420551800709119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.937 × 10⁹⁴(95-digit number)
29371243372318339828…27394841103601418239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.874 × 10⁹⁴(95-digit number)
58742486744636679657…54789682207202836479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.174 × 10⁹⁵(96-digit number)
11748497348927335931…09579364414405672959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.349 × 10⁹⁵(96-digit number)
23496994697854671863…19158728828811345919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.699 × 10⁹⁵(96-digit number)
46993989395709343726…38317457657622691839
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,564,195 XPM·at block #6,790,025 · updates every 60s