Block #2,473,967

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/15/2018, 9:26:43 AM · Difficulty 10.9633 · 4,370,863 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e98d4f1c0f5115232905afc7cc1edf283c3759cf3c6fb74dc560ac51e13045e

Height

#2,473,967

Difficulty

10.963269

Transactions

2

Size

1.86 KB

Version

2

Bits

0af698c7

Nonce

920,252,456

Timestamp

1/15/2018, 9:26:43 AM

Confirmations

4,370,863

Merkle Root

78efc37895723f1f668a040583e2e943c094958a0d80ded050c69afc691911fb
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.

2.689 × 10⁹⁴(95-digit number)
26894520736650014209…34078746804155217919
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
2.689 × 10⁹⁴(95-digit number)
26894520736650014209…34078746804155217919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.378 × 10⁹⁴(95-digit number)
53789041473300028419…68157493608310435839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.075 × 10⁹⁵(96-digit number)
10757808294660005683…36314987216620871679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.151 × 10⁹⁵(96-digit number)
21515616589320011367…72629974433241743359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.303 × 10⁹⁵(96-digit number)
43031233178640022735…45259948866483486719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.606 × 10⁹⁵(96-digit number)
86062466357280045471…90519897732966973439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.721 × 10⁹⁶(97-digit number)
17212493271456009094…81039795465933946879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.442 × 10⁹⁶(97-digit number)
34424986542912018188…62079590931867893759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.884 × 10⁹⁶(97-digit number)
68849973085824036377…24159181863735787519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.376 × 10⁹⁷(98-digit number)
13769994617164807275…48318363727471575039
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:58,003,049 XPM·at block #6,844,829 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy