Block #1,560,159

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/27/2016, 2:13:26 AM · Difficulty 10.7147 · 5,249,590 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5bcd47361fc3527b627bafa65b477e5f98e22c0269ccaada30daaaf7fe558cfa

Height

#1,560,159

Difficulty

10.714682

Transactions

2

Size

20.52 KB

Version

2

Bits

0ab6f56d

Nonce

30,785,914

Timestamp

4/27/2016, 2:13:26 AM

Confirmations

5,249,590

Merkle Root

b659d956c6a3fc410546884977be6ac43746f495df06be7abf2662dc708bfe3b
Transactions (2)
1 in → 1 out8.9200 XPM109 B
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.

9.646 × 10⁹⁶(97-digit number)
96463572761316379139…32012402728606883841
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
9.646 × 10⁹⁶(97-digit number)
96463572761316379139…32012402728606883841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.929 × 10⁹⁷(98-digit number)
19292714552263275827…64024805457213767681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.858 × 10⁹⁷(98-digit number)
38585429104526551655…28049610914427535361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.717 × 10⁹⁷(98-digit number)
77170858209053103311…56099221828855070721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.543 × 10⁹⁸(99-digit number)
15434171641810620662…12198443657710141441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.086 × 10⁹⁸(99-digit number)
30868343283621241324…24396887315420282881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.173 × 10⁹⁸(99-digit number)
61736686567242482649…48793774630840565761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.234 × 10⁹⁹(100-digit number)
12347337313448496529…97587549261681131521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.469 × 10⁹⁹(100-digit number)
24694674626896993059…95175098523362263041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.938 × 10⁹⁹(100-digit number)
49389349253793986119…90350197046724526081
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,722,077 XPM·at block #6,809,748 · updates every 60s
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