Block #1,960,825

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/30/2017, 4:08:35 AM · Difficulty 10.7423 · 4,869,939 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
89af568d4c25c76f4ab2d1a6dbedfd4d6e0e9409483b0f383ba9445b2312a7e1

Height

#1,960,825

Difficulty

10.742270

Transactions

2

Size

426 B

Version

2

Bits

0abe0564

Nonce

557,324,621

Timestamp

1/30/2017, 4:08:35 AM

Confirmations

4,869,939

Merkle Root

3487153c342e77c55d65a2b8b55126aefb80e9c3be1b7d8fcdfb9f3a642039cd
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.

2.297 × 10⁹⁴(95-digit number)
22975327055169232974…81111844954292669201
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
2.297 × 10⁹⁴(95-digit number)
22975327055169232974…81111844954292669201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.595 × 10⁹⁴(95-digit number)
45950654110338465949…62223689908585338401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.190 × 10⁹⁴(95-digit number)
91901308220676931899…24447379817170676801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.838 × 10⁹⁵(96-digit number)
18380261644135386379…48894759634341353601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.676 × 10⁹⁵(96-digit number)
36760523288270772759…97789519268682707201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.352 × 10⁹⁵(96-digit number)
73521046576541545519…95579038537365414401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.470 × 10⁹⁶(97-digit number)
14704209315308309103…91158077074730828801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.940 × 10⁹⁶(97-digit number)
29408418630616618207…82316154149461657601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.881 × 10⁹⁶(97-digit number)
58816837261233236415…64632308298923315201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.176 × 10⁹⁷(98-digit number)
11763367452246647283…29264616597846630401
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:57,890,248 XPM·at block #6,830,763 · updates every 60s
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