Block #2,260,446

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/20/2017, 5:42:55 PM · Difficulty 10.9518 · 4,571,488 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00aace20ad0e05bb1217be5a52585f2e258c1877dba9ec5ce8f3e04eefb336b2

Height

#2,260,446

Difficulty

10.951807

Transactions

4

Size

1.43 KB

Version

2

Bits

0af3a99b

Nonce

1,213,457,622

Timestamp

8/20/2017, 5:42:55 PM

Confirmations

4,571,488

Merkle Root

b4d120dc66344bdd9663fd85de4d0ca29317a1b1eda1a3ba3ec5f852646953df
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.

5.017 × 10⁹²(93-digit number)
50170612015240232904…77049980483003266241
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
5.017 × 10⁹²(93-digit number)
50170612015240232904…77049980483003266241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.003 × 10⁹³(94-digit number)
10034122403048046580…54099960966006532481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.006 × 10⁹³(94-digit number)
20068244806096093161…08199921932013064961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.013 × 10⁹³(94-digit number)
40136489612192186323…16399843864026129921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.027 × 10⁹³(94-digit number)
80272979224384372647…32799687728052259841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.605 × 10⁹⁴(95-digit number)
16054595844876874529…65599375456104519681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.210 × 10⁹⁴(95-digit number)
32109191689753749058…31198750912209039361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.421 × 10⁹⁴(95-digit number)
64218383379507498117…62397501824418078721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.284 × 10⁹⁵(96-digit number)
12843676675901499623…24795003648836157441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.568 × 10⁹⁵(96-digit number)
25687353351802999247…49590007297672314881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.137 × 10⁹⁵(96-digit number)
51374706703605998494…99180014595344629761
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:57,899,589 XPM·at block #6,831,933 · updates every 60s
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