Block #1,880,541

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/5/2016, 11:51:37 PM · Difficulty 10.6926 · 4,961,289 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e8b693ee6e035bb75755523c41b7fd8a92617c6cff406bea0802efe873d17c59

Height

#1,880,541

Difficulty

10.692629

Transactions

2

Size

574 B

Version

2

Bits

0ab1502a

Nonce

935,732,214

Timestamp

12/5/2016, 11:51:37 PM

Confirmations

4,961,289

Merkle Root

fdc131e1ce1aee9e718f3b84dd11ea3d7469778f30863e33d0f122d9fdad97c3
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.

1.261 × 10⁹²(93-digit number)
12611067000076948132…71273114148514872481
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
1.261 × 10⁹²(93-digit number)
12611067000076948132…71273114148514872481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.522 × 10⁹²(93-digit number)
25222134000153896265…42546228297029744961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.044 × 10⁹²(93-digit number)
50444268000307792530…85092456594059489921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.008 × 10⁹³(94-digit number)
10088853600061558506…70184913188118979841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.017 × 10⁹³(94-digit number)
20177707200123117012…40369826376237959681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.035 × 10⁹³(94-digit number)
40355414400246234024…80739652752475919361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.071 × 10⁹³(94-digit number)
80710828800492468048…61479305504951838721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.614 × 10⁹⁴(95-digit number)
16142165760098493609…22958611009903677441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.228 × 10⁹⁴(95-digit number)
32284331520196987219…45917222019807354881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.456 × 10⁹⁴(95-digit number)
64568663040393974438…91834444039614709761
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:57,979,013 XPM·at block #6,841,829 · updates every 60s
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