Block #3,551,611

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/9/2020, 8:34:15 PM · Difficulty 10.9288 · 3,293,736 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8ecea698fd30c2eb5ea01b8c0540a8f3a2bc33990f0507ba47aaa861ced0c256

Height

#3,551,611

Difficulty

10.928792

Transactions

2

Size

2.15 KB

Version

2

Bits

0aedc551

Nonce

177,844,031

Timestamp

2/9/2020, 8:34:15 PM

Confirmations

3,293,736

Merkle Root

870f38c5ec7c77b9f0a17d256d4344c92fc5aba303cbd17da9e84ecdbb2778c6
Transactions (2)
1 in → 1 out8.3900 XPM109 B
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.

3.585 × 10⁹⁶(97-digit number)
35857555802357194363…10473026708560414721
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
3.585 × 10⁹⁶(97-digit number)
35857555802357194363…10473026708560414721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.171 × 10⁹⁶(97-digit number)
71715111604714388726…20946053417120829441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.434 × 10⁹⁷(98-digit number)
14343022320942877745…41892106834241658881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.868 × 10⁹⁷(98-digit number)
28686044641885755490…83784213668483317761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.737 × 10⁹⁷(98-digit number)
57372089283771510981…67568427336966635521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.147 × 10⁹⁸(99-digit number)
11474417856754302196…35136854673933271041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.294 × 10⁹⁸(99-digit number)
22948835713508604392…70273709347866542081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.589 × 10⁹⁸(99-digit number)
45897671427017208784…40547418695733084161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.179 × 10⁹⁸(99-digit number)
91795342854034417569…81094837391466168321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.835 × 10⁹⁹(100-digit number)
18359068570806883513…62189674782932336641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.671 × 10⁹⁹(100-digit number)
36718137141613767027…24379349565864673281
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:58,007,218 XPM·at block #6,845,346 · updates every 60s
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