Block #2,446,441

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/28/2017, 6:54:32 PM · Difficulty 10.9424 · 4,394,692 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
90b7aabdf7cb6f95501b81a1adae697e7eb8d86eda2c8463a99037e8a46c75e2

Height

#2,446,441

Difficulty

10.942388

Transactions

2

Size

2.01 KB

Version

2

Bits

0af1405b

Nonce

335,873,203

Timestamp

12/28/2017, 6:54:32 PM

Confirmations

4,394,692

Merkle Root

b67d0b5b439f82500fa0e47ec5b899b90c2a45bc2a324b6e37ab417e4ef7f3f3
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.

3.888 × 10⁹⁶(97-digit number)
38880532088290152304…27829901588206223361
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
3.888 × 10⁹⁶(97-digit number)
38880532088290152304…27829901588206223361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.776 × 10⁹⁶(97-digit number)
77761064176580304609…55659803176412446721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.555 × 10⁹⁷(98-digit number)
15552212835316060921…11319606352824893441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.110 × 10⁹⁷(98-digit number)
31104425670632121843…22639212705649786881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.220 × 10⁹⁷(98-digit number)
62208851341264243687…45278425411299573761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.244 × 10⁹⁸(99-digit number)
12441770268252848737…90556850822599147521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.488 × 10⁹⁸(99-digit number)
24883540536505697475…81113701645198295041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.976 × 10⁹⁸(99-digit number)
49767081073011394950…62227403290396590081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.953 × 10⁹⁸(99-digit number)
99534162146022789900…24454806580793180161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.990 × 10⁹⁹(100-digit number)
19906832429204557980…48909613161586360321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.981 × 10⁹⁹(100-digit number)
39813664858409115960…97819226323172720641
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:57,973,433 XPM·at block #6,841,132 · updates every 60s
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