Block #2,110,093

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/10/2017, 1:38:18 PM · Difficulty 10.9020 · 4,728,705 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e5c7ce3fc64e7cf9f0568d8d97b317cab5ffbc70985def1d91389f19004c08e0

Height

#2,110,093

Difficulty

10.901962

Transactions

2

Size

426 B

Version

2

Bits

0ae6e6fc

Nonce

1,176,379,262

Timestamp

5/10/2017, 1:38:18 PM

Confirmations

4,728,705

Merkle Root

4e4e88155ccfc998dc29fbc3979dd9deaa4c9f9f2723bd06be03f423b9c12984
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.

3.566 × 10⁹⁴(95-digit number)
35665214299024905889…90017830895628346881
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
3.566 × 10⁹⁴(95-digit number)
35665214299024905889…90017830895628346881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.133 × 10⁹⁴(95-digit number)
71330428598049811779…80035661791256693761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.426 × 10⁹⁵(96-digit number)
14266085719609962355…60071323582513387521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.853 × 10⁹⁵(96-digit number)
28532171439219924711…20142647165026775041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.706 × 10⁹⁵(96-digit number)
57064342878439849423…40285294330053550081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.141 × 10⁹⁶(97-digit number)
11412868575687969884…80570588660107100161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.282 × 10⁹⁶(97-digit number)
22825737151375939769…61141177320214200321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.565 × 10⁹⁶(97-digit number)
45651474302751879539…22282354640428400641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.130 × 10⁹⁶(97-digit number)
91302948605503759078…44564709280856801281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.826 × 10⁹⁷(98-digit number)
18260589721100751815…89129418561713602561
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:57,954,648 XPM·at block #6,838,797 · updates every 60s
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