Block #601,545

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/25/2014, 3:21:17 PM · Difficulty 10.9143 · 6,197,928 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c37beb0cce93bb88661c1aecf981033e835f5f086814a918cbfa560e4eb39f6a

Height

#601,545

Difficulty

10.914285

Transactions

1

Size

561 B

Version

2

Bits

0aea0e9c

Nonce

278,595

Timestamp

6/25/2014, 3:21:17 PM

Confirmations

6,197,928

Merkle Root

42d8ce8a4f6bcf638aa0ada75f26faa53174661b07444cce70d008abadd6a2ae
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.

4.626 × 10⁹⁵(96-digit number)
46269658989817927369…52168287464709424641
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
4.626 × 10⁹⁵(96-digit number)
46269658989817927369…52168287464709424641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.253 × 10⁹⁵(96-digit number)
92539317979635854739…04336574929418849281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.850 × 10⁹⁶(97-digit number)
18507863595927170947…08673149858837698561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.701 × 10⁹⁶(97-digit number)
37015727191854341895…17346299717675397121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.403 × 10⁹⁶(97-digit number)
74031454383708683791…34692599435350794241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.480 × 10⁹⁷(98-digit number)
14806290876741736758…69385198870701588481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.961 × 10⁹⁷(98-digit number)
29612581753483473516…38770397741403176961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.922 × 10⁹⁷(98-digit number)
59225163506966947033…77540795482806353921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.184 × 10⁹⁸(99-digit number)
11845032701393389406…55081590965612707841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.369 × 10⁹⁸(99-digit number)
23690065402786778813…10163181931225415681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.738 × 10⁹⁸(99-digit number)
47380130805573557626…20326363862450831361
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:57,639,825 XPM·at block #6,799,472 · updates every 60s
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