Block #1,208,021

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/25/2015, 1:21:11 PM · Difficulty 10.7722 · 5,625,777 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
16ca2f21e6059dd5b3b656d66686b2a62dcf53becfa46357f0a3d9e1e44fe8bf

Height

#1,208,021

Difficulty

10.772183

Transactions

2

Size

434 B

Version

2

Bits

0ac5adc2

Nonce

61,871,795

Timestamp

8/25/2015, 1:21:11 PM

Confirmations

5,625,777

Merkle Root

afcf909336d35830168b21dde75b7a08eb8375007a23bbb6156ae8d73d98aeee
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.

2.508 × 10⁹⁶(97-digit number)
25088592071153604440…42326551410823714721
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
2.508 × 10⁹⁶(97-digit number)
25088592071153604440…42326551410823714721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.017 × 10⁹⁶(97-digit number)
50177184142307208880…84653102821647429441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.003 × 10⁹⁷(98-digit number)
10035436828461441776…69306205643294858881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.007 × 10⁹⁷(98-digit number)
20070873656922883552…38612411286589717761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.014 × 10⁹⁷(98-digit number)
40141747313845767104…77224822573179435521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.028 × 10⁹⁷(98-digit number)
80283494627691534208…54449645146358871041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.605 × 10⁹⁸(99-digit number)
16056698925538306841…08899290292717742081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.211 × 10⁹⁸(99-digit number)
32113397851076613683…17798580585435484161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.422 × 10⁹⁸(99-digit number)
64226795702153227367…35597161170870968321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.284 × 10⁹⁹(100-digit number)
12845359140430645473…71194322341741936641
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:57,914,606 XPM·at block #6,833,797 · updates every 60s
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