Block #2,644,524

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/2/2018, 1:08:05 PM · Difficulty 11.7111 · 4,186,460 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ce109a838bc312bb4f5b3d273426c27cf31cd5948bcbf20fecd78483d34df193

Height

#2,644,524

Difficulty

11.711148

Transactions

4

Size

876 B

Version

2

Bits

0bb60dd1

Nonce

1,123,383,649

Timestamp

5/2/2018, 1:08:05 PM

Confirmations

4,186,460

Merkle Root

b4daf384d09ffa26da472141ee68bd4ddaa70acb23f8c4ab28ed6b92281a4c1b
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.

3.112 × 10⁹⁵(96-digit number)
31126932151327950829…53355156739789311361
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
3.112 × 10⁹⁵(96-digit number)
31126932151327950829…53355156739789311361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.225 × 10⁹⁵(96-digit number)
62253864302655901658…06710313479578622721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.245 × 10⁹⁶(97-digit number)
12450772860531180331…13420626959157245441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.490 × 10⁹⁶(97-digit number)
24901545721062360663…26841253918314490881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.980 × 10⁹⁶(97-digit number)
49803091442124721326…53682507836628981761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.960 × 10⁹⁶(97-digit number)
99606182884249442653…07365015673257963521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.992 × 10⁹⁷(98-digit number)
19921236576849888530…14730031346515927041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.984 × 10⁹⁷(98-digit number)
39842473153699777061…29460062693031854081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.968 × 10⁹⁷(98-digit number)
79684946307399554122…58920125386063708161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.593 × 10⁹⁸(99-digit number)
15936989261479910824…17840250772127416321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.187 × 10⁹⁸(99-digit number)
31873978522959821649…35680501544254832641
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:57,892,013 XPM·at block #6,830,983 · 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