Block #1,079,699

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/28/2015, 9:38:52 AM · Difficulty 10.7649 · 5,725,103 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
23c29064b8fbb0ce605aad9b0977b0516fe08546657266ec4c2d867e5a3e4f61

Height

#1,079,699

Difficulty

10.764866

Transactions

5

Size

2.24 KB

Version

2

Bits

0ac3ce48

Nonce

1,341,293,321

Timestamp

5/28/2015, 9:38:52 AM

Confirmations

5,725,103

Merkle Root

f37500c19a26c37bd38682694c325cab75b9bf2dc95183344e9046cd562552ac
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.

7.989 × 10⁹⁶(97-digit number)
79895996475416398534…82788808684400051199
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
7.989 × 10⁹⁶(97-digit number)
79895996475416398534…82788808684400051199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.597 × 10⁹⁷(98-digit number)
15979199295083279706…65577617368800102399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.195 × 10⁹⁷(98-digit number)
31958398590166559413…31155234737600204799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.391 × 10⁹⁷(98-digit number)
63916797180333118827…62310469475200409599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.278 × 10⁹⁸(99-digit number)
12783359436066623765…24620938950400819199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.556 × 10⁹⁸(99-digit number)
25566718872133247530…49241877900801638399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.113 × 10⁹⁸(99-digit number)
51133437744266495061…98483755801603276799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.022 × 10⁹⁹(100-digit number)
10226687548853299012…96967511603206553599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.045 × 10⁹⁹(100-digit number)
20453375097706598024…93935023206413107199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.090 × 10⁹⁹(100-digit number)
40906750195413196049…87870046412826214399
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:57,682,483 XPM·at block #6,804,801 · 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.