Block #1,495,089

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/13/2016, 2:05:07 PM · Difficulty 10.6504 · 5,330,607 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b46e1c62a4bb4421acce3b3967d734266b20f8ac6a503e98cb7a4576258ea63

Height

#1,495,089

Difficulty

10.650402

Transactions

2

Size

1.51 KB

Version

2

Bits

0aa680c4

Nonce

1,264,899,677

Timestamp

3/13/2016, 2:05:07 PM

Confirmations

5,330,607

Merkle Root

c5d154abdd32ca1395caca27df7b7f769f4bcef7c1f8d4752e7cc86ea19f47ef
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.

9.854 × 10⁹⁴(95-digit number)
98547580505590886472…00816413032471295201
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
9.854 × 10⁹⁴(95-digit number)
98547580505590886472…00816413032471295201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.970 × 10⁹⁵(96-digit number)
19709516101118177294…01632826064942590401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.941 × 10⁹⁵(96-digit number)
39419032202236354589…03265652129885180801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.883 × 10⁹⁵(96-digit number)
78838064404472709178…06531304259770361601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.576 × 10⁹⁶(97-digit number)
15767612880894541835…13062608519540723201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.153 × 10⁹⁶(97-digit number)
31535225761789083671…26125217039081446401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.307 × 10⁹⁶(97-digit number)
63070451523578167342…52250434078162892801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.261 × 10⁹⁷(98-digit number)
12614090304715633468…04500868156325785601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.522 × 10⁹⁷(98-digit number)
25228180609431266936…09001736312651571201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.045 × 10⁹⁷(98-digit number)
50456361218862533873…18003472625303142401
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:57,849,680 XPM·at block #6,825,695 · updates every 60s
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