Block #2,022,219

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/14/2017, 6:16:35 AM · Difficulty 10.7097 · 4,795,612 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c5706f6ea5f8c422d7e68a8978663911cba51d9d4b107e99fe42b47ee82ebf22

Height

#2,022,219

Difficulty

10.709707

Transactions

3

Size

4.69 KB

Version

2

Bits

0ab5af58

Nonce

922,596,441

Timestamp

3/14/2017, 6:16:35 AM

Confirmations

4,795,612

Merkle Root

64e56efb60e8d4e7a7191a419054ab4562b94fc55a319aa0f45cba944718c0b7
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.

3.554 × 10⁹⁵(96-digit number)
35544037513477480754…43233305892422883841
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
3.554 × 10⁹⁵(96-digit number)
35544037513477480754…43233305892422883841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.108 × 10⁹⁵(96-digit number)
71088075026954961509…86466611784845767681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.421 × 10⁹⁶(97-digit number)
14217615005390992301…72933223569691535361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.843 × 10⁹⁶(97-digit number)
28435230010781984603…45866447139383070721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.687 × 10⁹⁶(97-digit number)
56870460021563969207…91732894278766141441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.137 × 10⁹⁷(98-digit number)
11374092004312793841…83465788557532282881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.274 × 10⁹⁷(98-digit number)
22748184008625587683…66931577115064565761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.549 × 10⁹⁷(98-digit number)
45496368017251175366…33863154230129131521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.099 × 10⁹⁷(98-digit number)
90992736034502350732…67726308460258263041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.819 × 10⁹⁸(99-digit number)
18198547206900470146…35452616920516526081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.639 × 10⁹⁸(99-digit number)
36397094413800940293…70905233841033052161
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:57,786,713 XPM·at block #6,817,830 · updates every 60s
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