Block #1,337,634

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/23/2015, 5:03:03 AM · Difficulty 10.7990 · 5,489,476 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e734e3b1c24ad9d4f1f2a8fae1edca92e100e20bd0fa29893be838f9a15ddeaf

Height

#1,337,634

Difficulty

10.798987

Transactions

2

Size

732 B

Version

2

Bits

0acc8a6e

Nonce

1,172,597,181

Timestamp

11/23/2015, 5:03:03 AM

Confirmations

5,489,476

Merkle Root

882ba377fbbc7aa6252b31484eb5d96406bafb9718b86f0e26f9b5a474227e28
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.

1.964 × 10⁹⁵(96-digit number)
19643926865558978088…31791552932879461121
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
1.964 × 10⁹⁵(96-digit number)
19643926865558978088…31791552932879461121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.928 × 10⁹⁵(96-digit number)
39287853731117956177…63583105865758922241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.857 × 10⁹⁵(96-digit number)
78575707462235912355…27166211731517844481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.571 × 10⁹⁶(97-digit number)
15715141492447182471…54332423463035688961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.143 × 10⁹⁶(97-digit number)
31430282984894364942…08664846926071377921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.286 × 10⁹⁶(97-digit number)
62860565969788729884…17329693852142755841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.257 × 10⁹⁷(98-digit number)
12572113193957745976…34659387704285511681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.514 × 10⁹⁷(98-digit number)
25144226387915491953…69318775408571023361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.028 × 10⁹⁷(98-digit number)
50288452775830983907…38637550817142046721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.005 × 10⁹⁸(99-digit number)
10057690555166196781…77275101634284093441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.011 × 10⁹⁸(99-digit number)
20115381110332393563…54550203268568186881
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,861,059 XPM·at block #6,827,109 · updates every 60s
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