Block #2,235,092

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/3/2017, 12:05:29 PM · Difficulty 10.9456 · 4,596,658 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b4d7ae719d1ab0dd94dba3098a40f142b6c8178615e5a9d10128981cd93fad4d

Height

#2,235,092

Difficulty

10.945571

Transactions

3

Size

1.65 KB

Version

2

Bits

0af210ee

Nonce

321,775,537

Timestamp

8/3/2017, 12:05:29 PM

Confirmations

4,596,658

Merkle Root

ab4978392ff3a649f72561d79d08c401207f17d2f0c982dda6447df20eff738b
Transactions (3)
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.

1.447 × 10⁹⁵(96-digit number)
14473090284569984645…34677123696355630241
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
1.447 × 10⁹⁵(96-digit number)
14473090284569984645…34677123696355630241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.894 × 10⁹⁵(96-digit number)
28946180569139969290…69354247392711260481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.789 × 10⁹⁵(96-digit number)
57892361138279938581…38708494785422520961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.157 × 10⁹⁶(97-digit number)
11578472227655987716…77416989570845041921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.315 × 10⁹⁶(97-digit number)
23156944455311975432…54833979141690083841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.631 × 10⁹⁶(97-digit number)
46313888910623950865…09667958283380167681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.262 × 10⁹⁶(97-digit number)
92627777821247901730…19335916566760335361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.852 × 10⁹⁷(98-digit number)
18525555564249580346…38671833133520670721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.705 × 10⁹⁷(98-digit number)
37051111128499160692…77343666267041341441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.410 × 10⁹⁷(98-digit number)
74102222256998321384…54687332534082682881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.482 × 10⁹⁸(99-digit number)
14820444451399664276…09374665068165365761
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:57,898,108 XPM·at block #6,831,749 · updates every 60s
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