Block #607,914

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/30/2014, 8:36:46 AM · Difficulty 10.9070 · 6,199,835 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
16a4893ae4d7b617da1b2dd7c872b85b9b5dd244ef6fb99b3204d87282e1aaa8

Height

#607,914

Difficulty

10.906980

Transactions

3

Size

1.66 KB

Version

2

Bits

0ae82fdd

Nonce

61,283,757

Timestamp

6/30/2014, 8:36:46 AM

Confirmations

6,199,835

Merkle Root

5a287d97a27fcba1a6fe2a65eeb9beba97a2080ba36ddb251df765c3679a42b4
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.

4.592 × 10⁹⁹(100-digit number)
45921945862041734368…43937163773731071999
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
4.592 × 10⁹⁹(100-digit number)
45921945862041734368…43937163773731071999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.184 × 10⁹⁹(100-digit number)
91843891724083468736…87874327547462143999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.836 × 10¹⁰⁰(101-digit number)
18368778344816693747…75748655094924287999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.673 × 10¹⁰⁰(101-digit number)
36737556689633387494…51497310189848575999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.347 × 10¹⁰⁰(101-digit number)
73475113379266774989…02994620379697151999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.469 × 10¹⁰¹(102-digit number)
14695022675853354997…05989240759394303999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.939 × 10¹⁰¹(102-digit number)
29390045351706709995…11978481518788607999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.878 × 10¹⁰¹(102-digit number)
58780090703413419991…23956963037577215999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.175 × 10¹⁰²(103-digit number)
11756018140682683998…47913926075154431999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.351 × 10¹⁰²(103-digit number)
23512036281365367996…95827852150308863999
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,706,020 XPM·at block #6,807,748 · updates every 60s
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