Block #1,441,010

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/3/2016, 3:03:57 PM · Difficulty 10.7643 · 5,396,090 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
520979c716f02b74e637268455f27fe26a085a94d9f36052c6344531dc16838e

Height

#1,441,010

Difficulty

10.764327

Transactions

2

Size

1.11 KB

Version

2

Bits

0ac3aaf3

Nonce

1,193,840,912

Timestamp

2/3/2016, 3:03:57 PM

Confirmations

5,396,090

Merkle Root

496db3680aa566305ba4ee53488185c5c3fbe1ce85c7f9e3604553dd80a4b313
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.

1.218 × 10⁹⁴(95-digit number)
12184621022855320744…52354452839001994971
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
1.218 × 10⁹⁴(95-digit number)
12184621022855320744…52354452839001994971
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.436 × 10⁹⁴(95-digit number)
24369242045710641489…04708905678003989941
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.873 × 10⁹⁴(95-digit number)
48738484091421282979…09417811356007979881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.747 × 10⁹⁴(95-digit number)
97476968182842565959…18835622712015959761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.949 × 10⁹⁵(96-digit number)
19495393636568513191…37671245424031919521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.899 × 10⁹⁵(96-digit number)
38990787273137026383…75342490848063839041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.798 × 10⁹⁵(96-digit number)
77981574546274052767…50684981696127678081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.559 × 10⁹⁶(97-digit number)
15596314909254810553…01369963392255356161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.119 × 10⁹⁶(97-digit number)
31192629818509621106…02739926784510712321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.238 × 10⁹⁶(97-digit number)
62385259637019242213…05479853569021424641
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:57,941,107 XPM·at block #6,837,099 · updates every 60s
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