Block #1,106,149

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/15/2015, 7:49:06 AM · Difficulty 10.7937 · 5,700,974 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3bc2528de5ad048fba1edda97d878e70bbafaa13d5f76ed96cdf21269e26305c

Height

#1,106,149

Difficulty

10.793662

Transactions

3

Size

25.75 KB

Version

2

Bits

0acb2d72

Nonce

1,628,840,859

Timestamp

6/15/2015, 7:49:06 AM

Confirmations

5,700,974

Merkle Root

d38b7536c1144b93a786f698e8989a5ad01d1f4dafa984d360ddefdc378c0fff
Transactions (3)
1 in → 1 out8.8700 XPM116 B
56 in → 1 out299.9900 XPM8.13 KB
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.

2.012 × 10⁹⁸(99-digit number)
20122622057551379866…95356975744362536959
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
2.012 × 10⁹⁸(99-digit number)
20122622057551379866…95356975744362536959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.024 × 10⁹⁸(99-digit number)
40245244115102759732…90713951488725073919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.049 × 10⁹⁸(99-digit number)
80490488230205519464…81427902977450147839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.609 × 10⁹⁹(100-digit number)
16098097646041103892…62855805954900295679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.219 × 10⁹⁹(100-digit number)
32196195292082207785…25711611909800591359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.439 × 10⁹⁹(100-digit number)
64392390584164415571…51423223819601182719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.287 × 10¹⁰⁰(101-digit number)
12878478116832883114…02846447639202365439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.575 × 10¹⁰⁰(101-digit number)
25756956233665766228…05692895278404730879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.151 × 10¹⁰⁰(101-digit number)
51513912467331532456…11385790556809461759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.030 × 10¹⁰¹(102-digit number)
10302782493466306491…22771581113618923519
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:57,701,087 XPM·at block #6,807,122 · updates every 60s
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