Block #1,370,337

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/15/2015, 2:10:58 PM · Difficulty 10.8185 · 5,442,499 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
78bf030ff8aaafa52f544729364c967d2fed40874ee55b6f0c25e42d86c80674

Height

#1,370,337

Difficulty

10.818536

Transactions

2

Size

1.05 KB

Version

2

Bits

0ad18b95

Nonce

1,184,686,356

Timestamp

12/15/2015, 2:10:58 PM

Confirmations

5,442,499

Merkle Root

8c042160e429ac1fe61da1b9b24dcc9ea105269edb1961e053a6aca3f39f9f50
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.

4.773 × 10⁹⁵(96-digit number)
47737433975871199736…26642978013053491199
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
4.773 × 10⁹⁵(96-digit number)
47737433975871199736…26642978013053491199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.547 × 10⁹⁵(96-digit number)
95474867951742399473…53285956026106982399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.909 × 10⁹⁶(97-digit number)
19094973590348479894…06571912052213964799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.818 × 10⁹⁶(97-digit number)
38189947180696959789…13143824104427929599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.637 × 10⁹⁶(97-digit number)
76379894361393919578…26287648208855859199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.527 × 10⁹⁷(98-digit number)
15275978872278783915…52575296417711718399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.055 × 10⁹⁷(98-digit number)
30551957744557567831…05150592835423436799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.110 × 10⁹⁷(98-digit number)
61103915489115135662…10301185670846873599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.222 × 10⁹⁸(99-digit number)
12220783097823027132…20602371341693747199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.444 × 10⁹⁸(99-digit number)
24441566195646054265…41204742683387494399
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:57,746,733 XPM·at block #6,812,835 · updates every 60s
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