Block #1,077,356

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/26/2015, 8:48:25 PM · Difficulty 10.7583 · 5,729,086 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0038ced3354ca39ec6ff61c6d910c61ba0b9313d803ad87275869200c631238a

Height

#1,077,356

Difficulty

10.758332

Transactions

4

Size

1023 B

Version

2

Bits

0ac22209

Nonce

2,110,101,454

Timestamp

5/26/2015, 8:48:25 PM

Confirmations

5,729,086

Merkle Root

4ee815de6d28b373e59ef63c73698581a94ba544bb5e7702b259f2863285b677
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.

2.007 × 10⁹⁷(98-digit number)
20074668893359910255…85643549734543523841
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
2.007 × 10⁹⁷(98-digit number)
20074668893359910255…85643549734543523841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.014 × 10⁹⁷(98-digit number)
40149337786719820511…71287099469087047681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.029 × 10⁹⁷(98-digit number)
80298675573439641023…42574198938174095361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.605 × 10⁹⁸(99-digit number)
16059735114687928204…85148397876348190721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.211 × 10⁹⁸(99-digit number)
32119470229375856409…70296795752696381441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.423 × 10⁹⁸(99-digit number)
64238940458751712818…40593591505392762881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.284 × 10⁹⁹(100-digit number)
12847788091750342563…81187183010785525761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.569 × 10⁹⁹(100-digit number)
25695576183500685127…62374366021571051521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.139 × 10⁹⁹(100-digit number)
51391152367001370255…24748732043142103041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.027 × 10¹⁰⁰(101-digit number)
10278230473400274051…49497464086284206081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.055 × 10¹⁰⁰(101-digit number)
20556460946800548102…98994928172568412161
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,695,625 XPM·at block #6,806,441 · updates every 60s
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