Block #1,569,055

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/2/2016, 5:04:05 PM · Difficulty 10.7572 · 5,257,856 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a9a8638d0fbb6c7a4309e1e4dee5c5a9bb017d84482438f64d042894ca022390

Height

#1,569,055

Difficulty

10.757197

Transactions

2

Size

1.01 KB

Version

2

Bits

0ac1d7a3

Nonce

822,430,107

Timestamp

5/2/2016, 5:04:05 PM

Confirmations

5,257,856

Merkle Root

e008e42fe0734e5bac1036eeb4c05e2e7239b25cff41ea7eab8ff233d9166cca
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.

1.647 × 10⁹⁶(97-digit number)
16471696108253846480…75563628413530716161
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
1.647 × 10⁹⁶(97-digit number)
16471696108253846480…75563628413530716161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.294 × 10⁹⁶(97-digit number)
32943392216507692961…51127256827061432321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.588 × 10⁹⁶(97-digit number)
65886784433015385923…02254513654122864641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.317 × 10⁹⁷(98-digit number)
13177356886603077184…04509027308245729281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.635 × 10⁹⁷(98-digit number)
26354713773206154369…09018054616491458561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.270 × 10⁹⁷(98-digit number)
52709427546412308738…18036109232982917121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.054 × 10⁹⁸(99-digit number)
10541885509282461747…36072218465965834241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.108 × 10⁹⁸(99-digit number)
21083771018564923495…72144436931931668481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.216 × 10⁹⁸(99-digit number)
42167542037129846990…44288873863863336961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.433 × 10⁹⁸(99-digit number)
84335084074259693981…88577747727726673921
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,859,457 XPM·at block #6,826,910 · updates every 60s
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