Block #3,015,601

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/19/2019, 12:40:09 AM · Difficulty 11.1766 · 3,809,049 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6f28cae1a627bb4fd04b42ce7e2e83b187b5d227ab98837ca8c5b474fc8dc6c7

Height

#3,015,601

Difficulty

11.176644

Transactions

4

Size

1.31 KB

Version

2

Bits

0b2d3886

Nonce

1,003,977,963

Timestamp

1/19/2019, 12:40:09 AM

Confirmations

3,809,049

Merkle Root

9daf65fa6593fe2a25484217006835bad5d40835760d60dd4247520753f31ee4
Transactions (4)
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.

9.381 × 10⁹⁶(97-digit number)
93811990112828418907…30007126098458132481
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
9.381 × 10⁹⁶(97-digit number)
93811990112828418907…30007126098458132481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.876 × 10⁹⁷(98-digit number)
18762398022565683781…60014252196916264961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.752 × 10⁹⁷(98-digit number)
37524796045131367563…20028504393832529921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.504 × 10⁹⁷(98-digit number)
75049592090262735126…40057008787665059841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.500 × 10⁹⁸(99-digit number)
15009918418052547025…80114017575330119681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.001 × 10⁹⁸(99-digit number)
30019836836105094050…60228035150660239361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.003 × 10⁹⁸(99-digit number)
60039673672210188100…20456070301320478721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.200 × 10⁹⁹(100-digit number)
12007934734442037620…40912140602640957441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.401 × 10⁹⁹(100-digit number)
24015869468884075240…81824281205281914881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.803 × 10⁹⁹(100-digit number)
48031738937768150480…63648562410563829761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.606 × 10⁹⁹(100-digit number)
96063477875536300961…27297124821127659521
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:57,841,265 XPM·at block #6,824,649 · updates every 60s
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