Block #1,070,450

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/22/2015, 6:54:39 AM · Difficulty 10.7427 · 5,737,376 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bd28649ccf0ce038f230ae649606a810f96fc6c6a755b0566d98b9ee9b051dbf

Height

#1,070,450

Difficulty

10.742672

Transactions

4

Size

876 B

Version

2

Bits

0abe1fc3

Nonce

646,096,200

Timestamp

5/22/2015, 6:54:39 AM

Confirmations

5,737,376

Merkle Root

287f11864de830cb7afadc1888f4d81165ab29b890c8c7cefa7b6e5e01727bfb
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.

1.498 × 10⁹⁷(98-digit number)
14986688283638797565…21340597493072527361
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
1.498 × 10⁹⁷(98-digit number)
14986688283638797565…21340597493072527361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.997 × 10⁹⁷(98-digit number)
29973376567277595131…42681194986145054721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.994 × 10⁹⁷(98-digit number)
59946753134555190263…85362389972290109441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.198 × 10⁹⁸(99-digit number)
11989350626911038052…70724779944580218881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.397 × 10⁹⁸(99-digit number)
23978701253822076105…41449559889160437761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.795 × 10⁹⁸(99-digit number)
47957402507644152210…82899119778320875521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.591 × 10⁹⁸(99-digit number)
95914805015288304421…65798239556641751041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.918 × 10⁹⁹(100-digit number)
19182961003057660884…31596479113283502081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.836 × 10⁹⁹(100-digit number)
38365922006115321768…63192958226567004161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.673 × 10⁹⁹(100-digit number)
76731844012230643537…26385916453134008321
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:57,706,643 XPM·at block #6,807,825 · updates every 60s
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