Block #377,274

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/27/2014, 12:07:06 AM · Difficulty 10.4225 · 6,437,026 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6552e4fca9e289cc53f67e1da03b9bc22a8995c6d63cc30ca09b599236d3916a

Height

#377,274

Difficulty

10.422492

Transactions

2

Size

432 B

Version

2

Bits

0a6c2868

Nonce

2,597

Timestamp

1/27/2014, 12:07:06 AM

Confirmations

6,437,026

Merkle Root

42504e27cb852a0dead7281c0ffc747144fdd4dd8ab415f5aee722e453d82bee
Transactions (2)
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.

2.294 × 10⁹⁴(95-digit number)
22945925593566570565…32264977124818350599
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
2.294 × 10⁹⁴(95-digit number)
22945925593566570565…32264977124818350599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.589 × 10⁹⁴(95-digit number)
45891851187133141130…64529954249636701199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.178 × 10⁹⁴(95-digit number)
91783702374266282261…29059908499273402399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.835 × 10⁹⁵(96-digit number)
18356740474853256452…58119816998546804799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.671 × 10⁹⁵(96-digit number)
36713480949706512904…16239633997093609599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.342 × 10⁹⁵(96-digit number)
73426961899413025809…32479267994187219199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.468 × 10⁹⁶(97-digit number)
14685392379882605161…64958535988374438399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.937 × 10⁹⁶(97-digit number)
29370784759765210323…29917071976748876799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.874 × 10⁹⁶(97-digit number)
58741569519530420647…59834143953497753599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.174 × 10⁹⁷(98-digit number)
11748313903906084129…19668287906995507199
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:57,758,464 XPM·at block #6,814,299 · updates every 60s
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