Block #1,220,428

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/3/2015, 5:07:50 PM · Difficulty 10.7345 · 5,619,242 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
38d5bb7c7c9c10269e3b6322e685493c7dc833f59512230ef86d890f6bc2a0dc

Height

#1,220,428

Difficulty

10.734509

Transactions

4

Size

1.15 KB

Version

2

Bits

0abc08c2

Nonce

592,637,074

Timestamp

9/3/2015, 5:07:50 PM

Confirmations

5,619,242

Merkle Root

03c2becdb85bf6b83856d124506cb6bda7812fbdeacb9a33d8ca19a6c0513431
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.

2.501 × 10⁹⁵(96-digit number)
25013846605706987675…71721779936230492161
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
2.501 × 10⁹⁵(96-digit number)
25013846605706987675…71721779936230492161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.002 × 10⁹⁵(96-digit number)
50027693211413975351…43443559872460984321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.000 × 10⁹⁶(97-digit number)
10005538642282795070…86887119744921968641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.001 × 10⁹⁶(97-digit number)
20011077284565590140…73774239489843937281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.002 × 10⁹⁶(97-digit number)
40022154569131180281…47548478979687874561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.004 × 10⁹⁶(97-digit number)
80044309138262360562…95096957959375749121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.600 × 10⁹⁷(98-digit number)
16008861827652472112…90193915918751498241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.201 × 10⁹⁷(98-digit number)
32017723655304944224…80387831837502996481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.403 × 10⁹⁷(98-digit number)
64035447310609888449…60775663675005992961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.280 × 10⁹⁸(99-digit number)
12807089462121977689…21551327350011985921
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:57,961,658 XPM·at block #6,839,669 · updates every 60s
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