Block #1,534,811

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2016, 11:58:14 AM · Difficulty 10.6183 · 5,274,089 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d897ff8d6d8c38afbe0414e83fa5d3129de66b5f39dccfc2108a5bfdb76627cd

Height

#1,534,811

Difficulty

10.618345

Transactions

3

Size

31.81 KB

Version

2

Bits

0a9e4bd6

Nonce

266,203,716

Timestamp

4/10/2016, 11:58:14 AM

Confirmations

5,274,089

Merkle Root

f526e398ce1fbaec397147681df7d061d0ed1df5bab8dfdc8d2b12dc9c668b6e
Transactions (3)
1 in → 1 out9.2300 XPM109 B
51 in → 1 out395.8407 XPM7.41 KB
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.

1.330 × 10⁹³(94-digit number)
13303491609149004678…20469544853697377491
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
1.330 × 10⁹³(94-digit number)
13303491609149004678…20469544853697377491
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.660 × 10⁹³(94-digit number)
26606983218298009357…40939089707394754981
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.321 × 10⁹³(94-digit number)
53213966436596018715…81878179414789509961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.064 × 10⁹⁴(95-digit number)
10642793287319203743…63756358829579019921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.128 × 10⁹⁴(95-digit number)
21285586574638407486…27512717659158039841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.257 × 10⁹⁴(95-digit number)
42571173149276814972…55025435318316079681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.514 × 10⁹⁴(95-digit number)
85142346298553629944…10050870636632159361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.702 × 10⁹⁵(96-digit number)
17028469259710725988…20101741273264318721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.405 × 10⁹⁵(96-digit number)
34056938519421451977…40203482546528637441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.811 × 10⁹⁵(96-digit number)
68113877038842903955…80406965093057274881
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:57,715,253 XPM·at block #6,808,899 · updates every 60s
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