Block #1,201,009

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/19/2015, 11:53:13 PM · Difficulty 10.8128 · 5,643,413 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
226b766cd336944a05d4b34b29d2ff91d0b658cd1cda50d10361fcd76976386d

Height

#1,201,009

Difficulty

10.812802

Transactions

4

Size

884 B

Version

2

Bits

0ad013c4

Nonce

8,325,235

Timestamp

8/19/2015, 11:53:13 PM

Confirmations

5,643,413

Merkle Root

bbbbc9f249b790caa6d628bf5b92dbcb4120bcdd5fb7630b213f6e1dc885933f
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.

4.082 × 10⁹⁴(95-digit number)
40828968504263996694…13474564232123129321
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
4.082 × 10⁹⁴(95-digit number)
40828968504263996694…13474564232123129321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.165 × 10⁹⁴(95-digit number)
81657937008527993388…26949128464246258641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.633 × 10⁹⁵(96-digit number)
16331587401705598677…53898256928492517281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.266 × 10⁹⁵(96-digit number)
32663174803411197355…07796513856985034561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.532 × 10⁹⁵(96-digit number)
65326349606822394711…15593027713970069121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.306 × 10⁹⁶(97-digit number)
13065269921364478942…31186055427940138241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.613 × 10⁹⁶(97-digit number)
26130539842728957884…62372110855880276481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.226 × 10⁹⁶(97-digit number)
52261079685457915768…24744221711760552961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.045 × 10⁹⁷(98-digit number)
10452215937091583153…49488443423521105921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.090 × 10⁹⁷(98-digit number)
20904431874183166307…98976886847042211841
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:57,999,771 XPM·at block #6,844,421 · updates every 60s
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