Block #1,226,803

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/8/2015, 3:11:16 AM · Difficulty 10.7354 · 5,582,904 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ad3d63c53b47cfc4cfb011e9ec7dee1f43915edf9459fb7f4fdc08f39a42508e

Height

#1,226,803

Difficulty

10.735371

Transactions

2

Size

573 B

Version

2

Bits

0abc414a

Nonce

699,467,059

Timestamp

9/8/2015, 3:11:16 AM

Confirmations

5,582,904

Merkle Root

2aba6f8f931d61cd0fdfb0da8f331df04f5c8ccee92069ace663c37d7bb855b1
Transactions (2)
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.

5.303 × 10⁹⁴(95-digit number)
53038965030033951491…12341422032715882819
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
5.303 × 10⁹⁴(95-digit number)
53038965030033951491…12341422032715882819
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.060 × 10⁹⁵(96-digit number)
10607793006006790298…24682844065431765639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.121 × 10⁹⁵(96-digit number)
21215586012013580596…49365688130863531279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.243 × 10⁹⁵(96-digit number)
42431172024027161192…98731376261727062559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.486 × 10⁹⁵(96-digit number)
84862344048054322385…97462752523454125119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.697 × 10⁹⁶(97-digit number)
16972468809610864477…94925505046908250239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.394 × 10⁹⁶(97-digit number)
33944937619221728954…89851010093816500479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.788 × 10⁹⁶(97-digit number)
67889875238443457908…79702020187633000959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.357 × 10⁹⁷(98-digit number)
13577975047688691581…59404040375266001919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.715 × 10⁹⁷(98-digit number)
27155950095377383163…18808080750532003839
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:57,721,735 XPM·at block #6,809,706 · updates every 60s
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