Block #1,611,453

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/2/2016, 8:41:00 PM · Difficulty 10.6063 · 5,229,705 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fbe4827ab3dcce96ebea907331f817dae70d7b0cefcdf8ee6eb3c6a861680d39

Height

#1,611,453

Difficulty

10.606325

Transactions

2

Size

1.11 KB

Version

2

Bits

0a9b3818

Nonce

1,940,081,115

Timestamp

6/2/2016, 8:41:00 PM

Confirmations

5,229,705

Merkle Root

a0dfd66dc2de6aeaedb5de581923e06b91f5604ac20c9e1fe71a128ee7ce4b3f
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.

4.642 × 10⁹⁶(97-digit number)
46425618553395071057…96315610659703423999
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
4.642 × 10⁹⁶(97-digit number)
46425618553395071057…96315610659703423999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.285 × 10⁹⁶(97-digit number)
92851237106790142115…92631221319406847999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.857 × 10⁹⁷(98-digit number)
18570247421358028423…85262442638813695999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.714 × 10⁹⁷(98-digit number)
37140494842716056846…70524885277627391999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.428 × 10⁹⁷(98-digit number)
74280989685432113692…41049770555254783999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.485 × 10⁹⁸(99-digit number)
14856197937086422738…82099541110509567999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.971 × 10⁹⁸(99-digit number)
29712395874172845476…64199082221019135999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.942 × 10⁹⁸(99-digit number)
59424791748345690953…28398164442038271999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.188 × 10⁹⁹(100-digit number)
11884958349669138190…56796328884076543999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.376 × 10⁹⁹(100-digit number)
23769916699338276381…13592657768153087999
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,973,628 XPM·at block #6,841,157 · updates every 60s
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