Block #1,108,229

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/15/2015, 9:53:43 PM · Difficulty 10.8385 · 5,718,356 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e631e99f43d89d24d1618fb29adc449e249a3274cf1e52bdd3f7cba26d0878ac

Height

#1,108,229

Difficulty

10.838479

Transactions

2

Size

2.01 KB

Version

2

Bits

0ad6a68a

Nonce

568,086,932

Timestamp

6/15/2015, 9:53:43 PM

Confirmations

5,718,356

Merkle Root

e36324b6a55da7baab5e1c51f5c2056947c416ceb37ee5b4979ca00c126605e7
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.

7.405 × 10⁹⁴(95-digit number)
74059915126070563264…86902754935813201279
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
7.405 × 10⁹⁴(95-digit number)
74059915126070563264…86902754935813201279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.481 × 10⁹⁵(96-digit number)
14811983025214112652…73805509871626402559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.962 × 10⁹⁵(96-digit number)
29623966050428225305…47611019743252805119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.924 × 10⁹⁵(96-digit number)
59247932100856450611…95222039486505610239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.184 × 10⁹⁶(97-digit number)
11849586420171290122…90444078973011220479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.369 × 10⁹⁶(97-digit number)
23699172840342580244…80888157946022440959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.739 × 10⁹⁶(97-digit number)
47398345680685160489…61776315892044881919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.479 × 10⁹⁶(97-digit number)
94796691361370320978…23552631784089763839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.895 × 10⁹⁷(98-digit number)
18959338272274064195…47105263568179527679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.791 × 10⁹⁷(98-digit number)
37918676544548128391…94210527136359055359
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:57,856,830 XPM·at block #6,826,584 · updates every 60s
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