Block #377,615

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 6:33:11 AM · Difficulty 10.4180 · 6,425,017 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f09f52ca0e6c3893dd28003b947b6281799be0c8cfc1763adfdd335bf905c748

Height

#377,615

Difficulty

10.417989

Transactions

1

Size

230 B

Version

2

Bits

0a6b0155

Nonce

32,401

Timestamp

1/27/2014, 6:33:11 AM

Confirmations

6,425,017

Merkle Root

31a157bf6e5c55153e96d5d20fdd47b0495140e8548d9052899dc52512e9536e
Transactions (1)
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.

2.620 × 10¹⁰¹(102-digit number)
26206314543096828848…45645001883661392801
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
2.620 × 10¹⁰¹(102-digit number)
26206314543096828848…45645001883661392801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.241 × 10¹⁰¹(102-digit number)
52412629086193657696…91290003767322785601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.048 × 10¹⁰²(103-digit number)
10482525817238731539…82580007534645571201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.096 × 10¹⁰²(103-digit number)
20965051634477463078…65160015069291142401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.193 × 10¹⁰²(103-digit number)
41930103268954926157…30320030138582284801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.386 × 10¹⁰²(103-digit number)
83860206537909852314…60640060277164569601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.677 × 10¹⁰³(104-digit number)
16772041307581970462…21280120554329139201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.354 × 10¹⁰³(104-digit number)
33544082615163940925…42560241108658278401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.708 × 10¹⁰³(104-digit number)
67088165230327881851…85120482217316556801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.341 × 10¹⁰⁴(105-digit number)
13417633046065576370…70240964434633113601
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:57,665,072 XPM·at block #6,802,631 · updates every 60s
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