Block #2,479,504

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2018, 11:43:45 PM · Difficulty 10.9660 · 4,361,305 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5ab59cfe377d4b35f6a031ce194efa389e527ae6b19bc8ce5c1a4a48150e42d9

Height

#2,479,504

Difficulty

10.965963

Transactions

4

Size

778 B

Version

2

Bits

0af74958

Nonce

655,509,076

Timestamp

1/18/2018, 11:43:45 PM

Confirmations

4,361,305

Merkle Root

32ad90b75e2e93814f97675a6166c894a22f3ec44641afe3c882df7a493cb351
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.

3.207 × 10⁹⁵(96-digit number)
32070684585847486513…26788542461032783041
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
3.207 × 10⁹⁵(96-digit number)
32070684585847486513…26788542461032783041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.414 × 10⁹⁵(96-digit number)
64141369171694973027…53577084922065566081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.282 × 10⁹⁶(97-digit number)
12828273834338994605…07154169844131132161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.565 × 10⁹⁶(97-digit number)
25656547668677989210…14308339688262264321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.131 × 10⁹⁶(97-digit number)
51313095337355978421…28616679376524528641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.026 × 10⁹⁷(98-digit number)
10262619067471195684…57233358753049057281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.052 × 10⁹⁷(98-digit number)
20525238134942391368…14466717506098114561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.105 × 10⁹⁷(98-digit number)
41050476269884782737…28933435012196229121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.210 × 10⁹⁷(98-digit number)
82100952539769565474…57866870024392458241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.642 × 10⁹⁸(99-digit number)
16420190507953913094…15733740048784916481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.284 × 10⁹⁸(99-digit number)
32840381015907826189…31467480097569832961
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:57,970,822 XPM·at block #6,840,808 · updates every 60s
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