Block #1,120,206

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/21/2015, 2:30:15 AM · Difficulty 10.9342 · 5,687,528 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7eee194aa3ec860f15f3e6d4e2c4d3a339ec171530a0e26ef88d75cd2594277f

Height

#1,120,206

Difficulty

10.934161

Transactions

3

Size

1.80 KB

Version

2

Bits

0aef252d

Nonce

618,430,975

Timestamp

6/21/2015, 2:30:15 AM

Confirmations

5,687,528

Merkle Root

462f97c035a7a7a4fe885257a989480b4e4a77f0e86b50367f82c1a67b2f46ea
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.

4.847 × 10⁹⁵(96-digit number)
48474126799780927946…09581038400801186561
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
4.847 × 10⁹⁵(96-digit number)
48474126799780927946…09581038400801186561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.694 × 10⁹⁵(96-digit number)
96948253599561855892…19162076801602373121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.938 × 10⁹⁶(97-digit number)
19389650719912371178…38324153603204746241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.877 × 10⁹⁶(97-digit number)
38779301439824742357…76648307206409492481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.755 × 10⁹⁶(97-digit number)
77558602879649484714…53296614412818984961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.551 × 10⁹⁷(98-digit number)
15511720575929896942…06593228825637969921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.102 × 10⁹⁷(98-digit number)
31023441151859793885…13186457651275939841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.204 × 10⁹⁷(98-digit number)
62046882303719587771…26372915302551879681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.240 × 10⁹⁸(99-digit number)
12409376460743917554…52745830605103759361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.481 × 10⁹⁸(99-digit number)
24818752921487835108…05491661210207518721
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:57,705,907 XPM·at block #6,807,733 · updates every 60s
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