Block #1,352,209

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/3/2015, 9:39:30 AM · Difficulty 10.7955 · 5,453,689 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d70249c65d3f4b2253ef60d98a0526379800d828b144b3e8eab47f9440f02e2e

Height

#1,352,209

Difficulty

10.795549

Transactions

5

Size

1.08 KB

Version

2

Bits

0acba91c

Nonce

558,900,048

Timestamp

12/3/2015, 9:39:30 AM

Confirmations

5,453,689

Merkle Root

86a9bc05fc77a0823a16f8ffc7c9d17a1700f4afac78e214f93f3b67e1a4665b
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.

8.904 × 10⁹⁴(95-digit number)
89049392704722718502…34008064485622784001
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
8.904 × 10⁹⁴(95-digit number)
89049392704722718502…34008064485622784001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.780 × 10⁹⁵(96-digit number)
17809878540944543700…68016128971245568001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.561 × 10⁹⁵(96-digit number)
35619757081889087401…36032257942491136001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.123 × 10⁹⁵(96-digit number)
71239514163778174802…72064515884982272001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.424 × 10⁹⁶(97-digit number)
14247902832755634960…44129031769964544001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.849 × 10⁹⁶(97-digit number)
28495805665511269920…88258063539929088001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.699 × 10⁹⁶(97-digit number)
56991611331022539841…76516127079858176001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.139 × 10⁹⁷(98-digit number)
11398322266204507968…53032254159716352001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.279 × 10⁹⁷(98-digit number)
22796644532409015936…06064508319432704001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.559 × 10⁹⁷(98-digit number)
45593289064818031873…12129016638865408001
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:57,691,271 XPM·at block #6,805,897 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.