Block #1,462,861

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/18/2016, 12:37:33 PM · Difficulty 10.7828 · 5,379,090 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
11bc89846d6a3d5add2f3c7a10804c5c902c6f91af3a348bd6c71b3a59c07ca0

Height

#1,462,861

Difficulty

10.782780

Transactions

2

Size

1.39 KB

Version

2

Bits

0ac86441

Nonce

646,361,482

Timestamp

2/18/2016, 12:37:33 PM

Confirmations

5,379,090

Merkle Root

26408a82bb466c7c023897f4b8aac2862ef98848fb5366006387aa07f9584f11
Transactions (2)
1 in → 1 out8.6400 XPM109 B
8 in → 1 out20786.9900 XPM1.20 KB
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.

7.351 × 10⁹²(93-digit number)
73512793503675483386…49513712955194752961
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
7.351 × 10⁹²(93-digit number)
73512793503675483386…49513712955194752961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.470 × 10⁹³(94-digit number)
14702558700735096677…99027425910389505921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.940 × 10⁹³(94-digit number)
29405117401470193354…98054851820779011841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.881 × 10⁹³(94-digit number)
58810234802940386708…96109703641558023681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.176 × 10⁹⁴(95-digit number)
11762046960588077341…92219407283116047361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.352 × 10⁹⁴(95-digit number)
23524093921176154683…84438814566232094721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.704 × 10⁹⁴(95-digit number)
47048187842352309367…68877629132464189441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.409 × 10⁹⁴(95-digit number)
94096375684704618734…37755258264928378881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.881 × 10⁹⁵(96-digit number)
18819275136940923746…75510516529856757761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.763 × 10⁹⁵(96-digit number)
37638550273881847493…51021033059713515521
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:57,979,988 XPM·at block #6,841,950 · updates every 60s
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