Block #2,024,073

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/15/2017, 1:09:18 PM · Difficulty 10.7099 · 4,803,073 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
614adaf489fa4be8722b043380c8fdef6fb19398c7ea86f6a845ec30e81802a3

Height

#2,024,073

Difficulty

10.709899

Transactions

2

Size

1.14 KB

Version

2

Bits

0ab5bbec

Nonce

176,395,600

Timestamp

3/15/2017, 1:09:18 PM

Confirmations

4,803,073

Merkle Root

11155111587c61a09b284fe68549dbea9e07eb15a69adb2e4961bd15a5b9e4f8
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.

8.475 × 10⁹⁵(96-digit number)
84758464540220581411…20389091149477399041
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
8.475 × 10⁹⁵(96-digit number)
84758464540220581411…20389091149477399041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.695 × 10⁹⁶(97-digit number)
16951692908044116282…40778182298954798081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.390 × 10⁹⁶(97-digit number)
33903385816088232564…81556364597909596161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.780 × 10⁹⁶(97-digit number)
67806771632176465129…63112729195819192321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.356 × 10⁹⁷(98-digit number)
13561354326435293025…26225458391638384641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.712 × 10⁹⁷(98-digit number)
27122708652870586051…52450916783276769281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.424 × 10⁹⁷(98-digit number)
54245417305741172103…04901833566553538561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.084 × 10⁹⁸(99-digit number)
10849083461148234420…09803667133107077121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.169 × 10⁹⁸(99-digit number)
21698166922296468841…19607334266214154241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.339 × 10⁹⁸(99-digit number)
43396333844592937682…39214668532428308481
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:57,861,351 XPM·at block #6,827,145 · updates every 60s
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