Block #3,220,809

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/11/2019, 11:44:54 AM · Difficulty 11.0580 · 3,606,082 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2e0421ab0d3c01e114eb8ea2c6fc7e8771fd1a6266fd40b064d8a6a303bcd35

Height

#3,220,809

Difficulty

11.057975

Transactions

2

Size

541 B

Version

2

Bits

0b0ed772

Nonce

33,926,250

Timestamp

6/11/2019, 11:44:54 AM

Confirmations

3,606,082

Merkle Root

112c46bfb29f0d6ce9e73ca4c6dd4052e9ca5a3588dbfce607183ba196ea7a64
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.

9.693 × 10⁹¹(92-digit number)
96934161087797471326…75404600463873411361
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
9.693 × 10⁹¹(92-digit number)
96934161087797471326…75404600463873411361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.938 × 10⁹²(93-digit number)
19386832217559494265…50809200927746822721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.877 × 10⁹²(93-digit number)
38773664435118988530…01618401855493645441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.754 × 10⁹²(93-digit number)
77547328870237977061…03236803710987290881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.550 × 10⁹³(94-digit number)
15509465774047595412…06473607421974581761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.101 × 10⁹³(94-digit number)
31018931548095190824…12947214843949163521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.203 × 10⁹³(94-digit number)
62037863096190381649…25894429687898327041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.240 × 10⁹⁴(95-digit number)
12407572619238076329…51788859375796654081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.481 × 10⁹⁴(95-digit number)
24815145238476152659…03577718751593308161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.963 × 10⁹⁴(95-digit number)
49630290476952305319…07155437503186616321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.926 × 10⁹⁴(95-digit number)
99260580953904610638…14310875006373232641
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:57,859,294 XPM·at block #6,826,890 · updates every 60s
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