Block #377,055

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/26/2014, 8:04:16 PM · Difficulty 10.4258 · 6,429,230 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
24e31f4fa113b4ec0091c5d0675d4f38db42ecccdd497bfcce06176b7c3493e6

Height

#377,055

Difficulty

10.425755

Transactions

4

Size

3.67 KB

Version

2

Bits

0a6cfe44

Nonce

89,538

Timestamp

1/26/2014, 8:04:16 PM

Confirmations

6,429,230

Merkle Root

09638bdb0d2395c0399dc96b69198bcb1345f206aa348dd4651e7e2acc75b328
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.

1.680 × 10⁹⁷(98-digit number)
16800269736342264040…33761288812885914559
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
1.680 × 10⁹⁷(98-digit number)
16800269736342264040…33761288812885914559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.360 × 10⁹⁷(98-digit number)
33600539472684528080…67522577625771829119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.720 × 10⁹⁷(98-digit number)
67201078945369056160…35045155251543658239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.344 × 10⁹⁸(99-digit number)
13440215789073811232…70090310503087316479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.688 × 10⁹⁸(99-digit number)
26880431578147622464…40180621006174632959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.376 × 10⁹⁸(99-digit number)
53760863156295244928…80361242012349265919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.075 × 10⁹⁹(100-digit number)
10752172631259048985…60722484024698531839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.150 × 10⁹⁹(100-digit number)
21504345262518097971…21444968049397063679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.300 × 10⁹⁹(100-digit number)
43008690525036195942…42889936098794127359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.601 × 10⁹⁹(100-digit number)
86017381050072391885…85779872197588254719
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:57,694,366 XPM·at block #6,806,284 · updates every 60s
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