Block #2,853,147

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/24/2018, 10:09:30 AM · Difficulty 11.7176 · 3,992,196 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a69643f4cd1a59399c5c979fb31a8249a5778207328cf05ab946cfe691989c0

Height

#2,853,147

Difficulty

11.717606

Transactions

3

Size

8.41 KB

Version

2

Bits

0bb7b500

Nonce

2,033,237,518

Timestamp

9/24/2018, 10:09:30 AM

Confirmations

3,992,196

Merkle Root

b153027d035c1d80ffb5f6241870901f1bdbb52fa8c9b3010c72a7cb3a8e9cfa
Transactions (3)
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.

3.124 × 10⁹⁶(97-digit number)
31246577791116248646…42647037460378414721
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
3.124 × 10⁹⁶(97-digit number)
31246577791116248646…42647037460378414721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.249 × 10⁹⁶(97-digit number)
62493155582232497293…85294074920756829441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.249 × 10⁹⁷(98-digit number)
12498631116446499458…70588149841513658881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.499 × 10⁹⁷(98-digit number)
24997262232892998917…41176299683027317761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.999 × 10⁹⁷(98-digit number)
49994524465785997835…82352599366054635521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.998 × 10⁹⁷(98-digit number)
99989048931571995670…64705198732109271041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.999 × 10⁹⁸(99-digit number)
19997809786314399134…29410397464218542081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.999 × 10⁹⁸(99-digit number)
39995619572628798268…58820794928437084161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.999 × 10⁹⁸(99-digit number)
79991239145257596536…17641589856874168321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.599 × 10⁹⁹(100-digit number)
15998247829051519307…35283179713748336641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.199 × 10⁹⁹(100-digit number)
31996495658103038614…70566359427496673281
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:58,007,185 XPM·at block #6,845,342 · updates every 60s
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