Block #2,696,439

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/8/2018, 2:44:31 AM · Difficulty 11.6674 · 4,144,652 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6739170a03cf166c5a77659934bc18a95cca6d563209f308554739d44f4ac7a2

Height

#2,696,439

Difficulty

11.667424

Transactions

2

Size

425 B

Version

2

Bits

0baadc46

Nonce

1,659,241,879

Timestamp

6/8/2018, 2:44:31 AM

Confirmations

4,144,652

Merkle Root

3e28a4d24b72bba86b8053ef36cb72cd4b507952d961a3c4e85e86e6c7acd859
Transactions (2)
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.

9.856 × 10⁹¹(92-digit number)
98564546951778683579…38317934056257464321
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
9.856 × 10⁹¹(92-digit number)
98564546951778683579…38317934056257464321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.971 × 10⁹²(93-digit number)
19712909390355736715…76635868112514928641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.942 × 10⁹²(93-digit number)
39425818780711473431…53271736225029857281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.885 × 10⁹²(93-digit number)
78851637561422946863…06543472450059714561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.577 × 10⁹³(94-digit number)
15770327512284589372…13086944900119429121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.154 × 10⁹³(94-digit number)
31540655024569178745…26173889800238858241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.308 × 10⁹³(94-digit number)
63081310049138357490…52347779600477716481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.261 × 10⁹⁴(95-digit number)
12616262009827671498…04695559200955432961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.523 × 10⁹⁴(95-digit number)
25232524019655342996…09391118401910865921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.046 × 10⁹⁴(95-digit number)
50465048039310685992…18782236803821731841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.009 × 10⁹⁵(96-digit number)
10093009607862137198…37564473607643463681
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,973,092 XPM·at block #6,841,090 · updates every 60s
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