Block #377,909

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/27/2014, 11:13:06 AM · Difficulty 10.4198 · 6,421,420 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
148f46112c0f8f251f2f5ed2de1e0e3575efae49887470e21c56c408f393637b

Height

#377,909

Difficulty

10.419840

Transactions

3

Size

954 B

Version

2

Bits

0a6b7a9b

Nonce

1,649

Timestamp

1/27/2014, 11:13:06 AM

Confirmations

6,421,420

Merkle Root

75761937c5212e07911f397fadeb40e577e6e57514e16434fb313102f3ce919f
Transactions (3)
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.

8.295 × 10⁹⁴(95-digit number)
82950230973333055050…30393721030696404479
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
8.295 × 10⁹⁴(95-digit number)
82950230973333055050…30393721030696404479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.659 × 10⁹⁵(96-digit number)
16590046194666611010…60787442061392808959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.318 × 10⁹⁵(96-digit number)
33180092389333222020…21574884122785617919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.636 × 10⁹⁵(96-digit number)
66360184778666444040…43149768245571235839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.327 × 10⁹⁶(97-digit number)
13272036955733288808…86299536491142471679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.654 × 10⁹⁶(97-digit number)
26544073911466577616…72599072982284943359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.308 × 10⁹⁶(97-digit number)
53088147822933155232…45198145964569886719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.061 × 10⁹⁷(98-digit number)
10617629564586631046…90396291929139773439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.123 × 10⁹⁷(98-digit number)
21235259129173262092…80792583858279546879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.247 × 10⁹⁷(98-digit number)
42470518258346524185…61585167716559093759
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,638,682 XPM·at block #6,799,328 · updates every 60s
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