Block #2,340,234

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/17/2017, 10:44:13 AM · Difficulty 10.9107 · 4,502,919 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e8d06ad0ab2c9f583e2f88334e6ac1d083e456063ef7ea6e0e242d60a56c820a

Height

#2,340,234

Difficulty

10.910743

Transactions

5

Size

1.06 KB

Version

2

Bits

0ae92674

Nonce

65,084,986

Timestamp

10/17/2017, 10:44:13 AM

Confirmations

4,502,919

Merkle Root

c44b8ef48e774522ee874ec1050e5480310931a9c3fa0b2b25be6621a67c5b06
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.

9.883 × 10⁹⁶(97-digit number)
98834634293856504354…29940455658324695041
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
9.883 × 10⁹⁶(97-digit number)
98834634293856504354…29940455658324695041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.976 × 10⁹⁷(98-digit number)
19766926858771300870…59880911316649390081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.953 × 10⁹⁷(98-digit number)
39533853717542601741…19761822633298780161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.906 × 10⁹⁷(98-digit number)
79067707435085203483…39523645266597560321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.581 × 10⁹⁸(99-digit number)
15813541487017040696…79047290533195120641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.162 × 10⁹⁸(99-digit number)
31627082974034081393…58094581066390241281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.325 × 10⁹⁸(99-digit number)
63254165948068162786…16189162132780482561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.265 × 10⁹⁹(100-digit number)
12650833189613632557…32378324265560965121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.530 × 10⁹⁹(100-digit number)
25301666379227265114…64756648531121930241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.060 × 10⁹⁹(100-digit number)
50603332758454530229…29513297062243860481
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:57,989,590 XPM·at block #6,843,152 · updates every 60s
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