Block #1,208,005

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/25/2015, 12:58:57 PM · Difficulty 10.7725 · 5,625,784 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cb0a9c73a00af3d8c7cb8171cfc277c5f95a0ca44c728576bbee73d4d3bfd5b4

Height

#1,208,005

Difficulty

10.772455

Transactions

2

Size

425 B

Version

2

Bits

0ac5bfa3

Nonce

414,364,607

Timestamp

8/25/2015, 12:58:57 PM

Confirmations

5,625,784

Merkle Root

ac134df038e6399bed17eef0cdddcbd311e91010955b88bda3e3e9fb100fcbe3
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.

4.377 × 10⁹⁵(96-digit number)
43778772689205906705…45519019785582931199
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
4.377 × 10⁹⁵(96-digit number)
43778772689205906705…45519019785582931199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.755 × 10⁹⁵(96-digit number)
87557545378411813411…91038039571165862399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.751 × 10⁹⁶(97-digit number)
17511509075682362682…82076079142331724799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.502 × 10⁹⁶(97-digit number)
35023018151364725364…64152158284663449599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.004 × 10⁹⁶(97-digit number)
70046036302729450729…28304316569326899199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.400 × 10⁹⁷(98-digit number)
14009207260545890145…56608633138653798399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.801 × 10⁹⁷(98-digit number)
28018414521091780291…13217266277307596799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.603 × 10⁹⁷(98-digit number)
56036829042183560583…26434532554615193599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.120 × 10⁹⁸(99-digit number)
11207365808436712116…52869065109230387199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.241 × 10⁹⁸(99-digit number)
22414731616873424233…05738130218460774399
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:57,914,532 XPM·at block #6,833,788 · 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