Block #376,333

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/26/2014, 8:25:34 AM · Difficulty 10.4231 · 6,439,930 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3c3e10d4af5597639bb3435aaf65754aedc6091f489cc320e29193cbef93f035

Height

#376,333

Difficulty

10.423142

Transactions

1

Size

834 B

Version

2

Bits

0a6c5307

Nonce

201,650

Timestamp

1/26/2014, 8:25:34 AM

Confirmations

6,439,930

Merkle Root

c94991c20283f9645a9f5c74f4b5ada0a84efd268847e04cc5a907ebcfc674e5
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.

2.026 × 10⁹⁶(97-digit number)
20268508727419552165…90836119545328312321
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
2.026 × 10⁹⁶(97-digit number)
20268508727419552165…90836119545328312321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.053 × 10⁹⁶(97-digit number)
40537017454839104331…81672239090656624641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.107 × 10⁹⁶(97-digit number)
81074034909678208663…63344478181313249281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.621 × 10⁹⁷(98-digit number)
16214806981935641732…26688956362626498561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.242 × 10⁹⁷(98-digit number)
32429613963871283465…53377912725252997121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.485 × 10⁹⁷(98-digit number)
64859227927742566931…06755825450505994241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.297 × 10⁹⁸(99-digit number)
12971845585548513386…13511650901011988481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.594 × 10⁹⁸(99-digit number)
25943691171097026772…27023301802023976961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.188 × 10⁹⁸(99-digit number)
51887382342194053544…54046603604047953921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.037 × 10⁹⁹(100-digit number)
10377476468438810708…08093207208095907841
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:57,774,217 XPM·at block #6,816,262 · updates every 60s
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