Block #377,351

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 1:32:27 AM · Difficulty 10.4229 · 6,449,317 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8bf0de0b5740accfee624c1811977dd1c7843f9ece8e611068581b2fd9d77b91

Height

#377,351

Difficulty

10.422890

Transactions

6

Size

2.93 KB

Version

2

Bits

0a6c428d

Nonce

384,677

Timestamp

1/27/2014, 1:32:27 AM

Confirmations

6,449,317

Merkle Root

d753c2dbce0e362dda8d677024b21e626e3858ef0fdba4c027af2f2ccc023689
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.

2.683 × 10⁹⁸(99-digit number)
26831124148640134205…61867794951059518541
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
2.683 × 10⁹⁸(99-digit number)
26831124148640134205…61867794951059518541
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.366 × 10⁹⁸(99-digit number)
53662248297280268410…23735589902119037081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.073 × 10⁹⁹(100-digit number)
10732449659456053682…47471179804238074161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.146 × 10⁹⁹(100-digit number)
21464899318912107364…94942359608476148321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.292 × 10⁹⁹(100-digit number)
42929798637824214728…89884719216952296641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.585 × 10⁹⁹(100-digit number)
85859597275648429457…79769438433904593281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.717 × 10¹⁰⁰(101-digit number)
17171919455129685891…59538876867809186561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.434 × 10¹⁰⁰(101-digit number)
34343838910259371782…19077753735618373121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.868 × 10¹⁰⁰(101-digit number)
68687677820518743565…38155507471236746241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.373 × 10¹⁰¹(102-digit number)
13737535564103748713…76311014942473492481
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:57,857,491 XPM·at block #6,826,667 · updates every 60s
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