Block #2,470,692

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/13/2018, 7:22:10 AM · Difficulty 10.9611 · 4,370,386 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fca6e65dc3ef04a762509c11b6bf6e7887ea5a9ca03da8e32b8cc1d1d8c8b11a

Height

#2,470,692

Difficulty

10.961137

Transactions

2

Size

572 B

Version

2

Bits

0af60d0e

Nonce

612,124,205

Timestamp

1/13/2018, 7:22:10 AM

Confirmations

4,370,386

Merkle Root

c99691acdf39c502cfe57e774c9c66954c9d284bb62e3d207f61874056a4492c
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.

1.987 × 10⁹³(94-digit number)
19874881705636622409…24597118927129969921
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
1.987 × 10⁹³(94-digit number)
19874881705636622409…24597118927129969921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.974 × 10⁹³(94-digit number)
39749763411273244818…49194237854259939841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.949 × 10⁹³(94-digit number)
79499526822546489636…98388475708519879681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.589 × 10⁹⁴(95-digit number)
15899905364509297927…96776951417039759361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.179 × 10⁹⁴(95-digit number)
31799810729018595854…93553902834079518721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.359 × 10⁹⁴(95-digit number)
63599621458037191709…87107805668159037441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.271 × 10⁹⁵(96-digit number)
12719924291607438341…74215611336318074881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.543 × 10⁹⁵(96-digit number)
25439848583214876683…48431222672636149761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.087 × 10⁹⁵(96-digit number)
50879697166429753367…96862445345272299521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.017 × 10⁹⁶(97-digit number)
10175939433285950673…93724890690544599041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.035 × 10⁹⁶(97-digit number)
20351878866571901347…87449781381089198081
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:57,972,986 XPM·at block #6,841,077 · updates every 60s
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