Block #1,010,130

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2015, 2:48:46 PM · Difficulty 10.7241 · 5,799,592 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
52077c9241b0400afd6e467d5daa887d213c7586414e0b7ded96e9e722e6d9d8

Height

#1,010,130

Difficulty

10.724051

Transactions

3

Size

652 B

Version

2

Bits

0ab95b66

Nonce

1,590,935,840

Timestamp

4/10/2015, 2:48:46 PM

Confirmations

5,799,592

Merkle Root

67efcdc840527450003251bfa48a95762261bdb9bd3acca4191c98108882f769
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.

1.754 × 10⁹⁴(95-digit number)
17547540579426072725…11152518910505199941
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
1.754 × 10⁹⁴(95-digit number)
17547540579426072725…11152518910505199941
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.509 × 10⁹⁴(95-digit number)
35095081158852145451…22305037821010399881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.019 × 10⁹⁴(95-digit number)
70190162317704290903…44610075642020799761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.403 × 10⁹⁵(96-digit number)
14038032463540858180…89220151284041599521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.807 × 10⁹⁵(96-digit number)
28076064927081716361…78440302568083199041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.615 × 10⁹⁵(96-digit number)
56152129854163432722…56880605136166398081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.123 × 10⁹⁶(97-digit number)
11230425970832686544…13761210272332796161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.246 × 10⁹⁶(97-digit number)
22460851941665373089…27522420544665592321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.492 × 10⁹⁶(97-digit number)
44921703883330746178…55044841089331184641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.984 × 10⁹⁶(97-digit number)
89843407766661492356…10089682178662369281
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:57,721,857 XPM·at block #6,809,721 · updates every 60s
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