Block #1,068,648

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/21/2015, 1:53:53 AM · Difficulty 10.7395 · 5,725,497 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
746877ba101713f2a7d6398141e716f1aee9fb8271a3ee06b8aa445342470172

Height

#1,068,648

Difficulty

10.739480

Transactions

2

Size

581 B

Version

2

Bits

0abd4e8c

Nonce

214,979,607

Timestamp

5/21/2015, 1:53:53 AM

Confirmations

5,725,497

Merkle Root

d6d6e4a6d0cb9842e4c9c5ce3b0178c3f8d86173124fa9dd520ca2d13260cef6
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.

7.560 × 10⁹⁵(96-digit number)
75600995388860044829…91556204150906794401
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
7.560 × 10⁹⁵(96-digit number)
75600995388860044829…91556204150906794401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.512 × 10⁹⁶(97-digit number)
15120199077772008965…83112408301813588801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.024 × 10⁹⁶(97-digit number)
30240398155544017931…66224816603627177601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.048 × 10⁹⁶(97-digit number)
60480796311088035863…32449633207254355201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.209 × 10⁹⁷(98-digit number)
12096159262217607172…64899266414508710401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.419 × 10⁹⁷(98-digit number)
24192318524435214345…29798532829017420801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.838 × 10⁹⁷(98-digit number)
48384637048870428691…59597065658034841601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.676 × 10⁹⁷(98-digit number)
96769274097740857382…19194131316069683201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.935 × 10⁹⁸(99-digit number)
19353854819548171476…38388262632139366401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.870 × 10⁹⁸(99-digit number)
38707709639096342952…76776525264278732801
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:57,597,188 XPM·at block #6,794,144 · updates every 60s
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