Block #530,518

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/7/2014, 10:21:00 PM · Difficulty 10.8923 · 6,284,410 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a2636a8db5046a10465880b7e28b8ad2fb032264f98e1ca9574c261e54c06c92

Height

#530,518

Difficulty

10.892339

Transactions

1

Size

766 B

Version

2

Bits

0ae47054

Nonce

46,073

Timestamp

5/7/2014, 10:21:00 PM

Confirmations

6,284,410

Merkle Root

1bfcdb397d8f690a39f2a74544c8d988ac42ea32768de689339ab2ac7d5edd52
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.

4.992 × 10⁹⁷(98-digit number)
49923148230988170162…83689982660290660681
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
4.992 × 10⁹⁷(98-digit number)
49923148230988170162…83689982660290660681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.984 × 10⁹⁷(98-digit number)
99846296461976340325…67379965320581321361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.996 × 10⁹⁸(99-digit number)
19969259292395268065…34759930641162642721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.993 × 10⁹⁸(99-digit number)
39938518584790536130…69519861282325285441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.987 × 10⁹⁸(99-digit number)
79877037169581072260…39039722564650570881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.597 × 10⁹⁹(100-digit number)
15975407433916214452…78079445129301141761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.195 × 10⁹⁹(100-digit number)
31950814867832428904…56158890258602283521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.390 × 10⁹⁹(100-digit number)
63901629735664857808…12317780517204567041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.278 × 10¹⁰⁰(101-digit number)
12780325947132971561…24635561034409134081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.556 × 10¹⁰⁰(101-digit number)
25560651894265943123…49271122068818268161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.112 × 10¹⁰⁰(101-digit number)
51121303788531886246…98542244137636536321
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:57,763,518 XPM·at block #6,814,927 · 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.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy