Block #1,223,881

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/6/2015, 12:33:25 AM · Difficulty 10.7413 · 5,590,160 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be172b94ed7d458dfbbb405727762764baf101ad36514e03f3dea2b342b40e26

Height

#1,223,881

Difficulty

10.741255

Transactions

3

Size

3.89 KB

Version

2

Bits

0abdc2dd

Nonce

14,397,271

Timestamp

9/6/2015, 12:33:25 AM

Confirmations

5,590,160

Merkle Root

3508168e7293f9813bfb5e1061a09b671d90c9b22f60a03eb99af65d97bcf8f5
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.

3.600 × 10⁹⁶(97-digit number)
36000724608776652424…78227071679948431359
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
3.600 × 10⁹⁶(97-digit number)
36000724608776652424…78227071679948431359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.200 × 10⁹⁶(97-digit number)
72001449217553304849…56454143359896862719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.440 × 10⁹⁷(98-digit number)
14400289843510660969…12908286719793725439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.880 × 10⁹⁷(98-digit number)
28800579687021321939…25816573439587450879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.760 × 10⁹⁷(98-digit number)
57601159374042643879…51633146879174901759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.152 × 10⁹⁸(99-digit number)
11520231874808528775…03266293758349803519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.304 × 10⁹⁸(99-digit number)
23040463749617057551…06532587516699607039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.608 × 10⁹⁸(99-digit number)
46080927499234115103…13065175033399214079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.216 × 10⁹⁸(99-digit number)
92161854998468230207…26130350066798428159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.843 × 10⁹⁹(100-digit number)
18432370999693646041…52260700133596856319
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:57,756,403 XPM·at block #6,814,040 · updates every 60s
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