Block #1,133,444

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/30/2015, 3:02:29 AM · Difficulty 10.9377 · 5,681,408 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
159f229d33962625ad8993df133e90fc33f19c7536f19ebc2d6fc99d776bde54

Height

#1,133,444

Difficulty

10.937665

Transactions

3

Size

14.08 KB

Version

2

Bits

0af00ad8

Nonce

412,615,486

Timestamp

6/30/2015, 3:02:29 AM

Confirmations

5,681,408

Merkle Root

23b3329bcc3625a68271076d48cba344c13096989b91ffdcf7d80c3b20e14413
Transactions (3)
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.

2.856 × 10⁹⁴(95-digit number)
28560207646125347062…55488233642695807761
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
2.856 × 10⁹⁴(95-digit number)
28560207646125347062…55488233642695807761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.712 × 10⁹⁴(95-digit number)
57120415292250694125…10976467285391615521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.142 × 10⁹⁵(96-digit number)
11424083058450138825…21952934570783231041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.284 × 10⁹⁵(96-digit number)
22848166116900277650…43905869141566462081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.569 × 10⁹⁵(96-digit number)
45696332233800555300…87811738283132924161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.139 × 10⁹⁵(96-digit number)
91392664467601110600…75623476566265848321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.827 × 10⁹⁶(97-digit number)
18278532893520222120…51246953132531696641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.655 × 10⁹⁶(97-digit number)
36557065787040444240…02493906265063393281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.311 × 10⁹⁶(97-digit number)
73114131574080888480…04987812530126786561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.462 × 10⁹⁷(98-digit number)
14622826314816177696…09975625060253573121
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,762,899 XPM·at block #6,814,851 · updates every 60s
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