Block #695,070

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/27/2014, 9:06:55 AM · Difficulty 10.9574 · 6,115,994 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb1e64a45c789a47ec5be4aa22f686a9cfbf44fa461826c11330a8b24a28eb52

Height

#695,070

Difficulty

10.957358

Transactions

2

Size

433 B

Version

2

Bits

0af51562

Nonce

33,484,458

Timestamp

8/27/2014, 9:06:55 AM

Confirmations

6,115,994

Merkle Root

18357811177beba3a918cab286564afac3d127c4e5555c6b8f08e870b2290547
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.

3.880 × 10⁹⁶(97-digit number)
38800955564132065658…38291286032531216641
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
3.880 × 10⁹⁶(97-digit number)
38800955564132065658…38291286032531216641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.760 × 10⁹⁶(97-digit number)
77601911128264131316…76582572065062433281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.552 × 10⁹⁷(98-digit number)
15520382225652826263…53165144130124866561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.104 × 10⁹⁷(98-digit number)
31040764451305652526…06330288260249733121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.208 × 10⁹⁷(98-digit number)
62081528902611305052…12660576520499466241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.241 × 10⁹⁸(99-digit number)
12416305780522261010…25321153040998932481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.483 × 10⁹⁸(99-digit number)
24832611561044522021…50642306081997864961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.966 × 10⁹⁸(99-digit number)
49665223122089044042…01284612163995729921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.933 × 10⁹⁸(99-digit number)
99330446244178088084…02569224327991459841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.986 × 10⁹⁹(100-digit number)
19866089248835617616…05138448655982919681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.973 × 10⁹⁹(100-digit number)
39732178497671235233…10276897311965839361
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:57,732,618 XPM·at block #6,811,063 · updates every 60s
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