Block #377,851

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/27/2014, 10:27:38 AM · Difficulty 10.4183 · 6,428,604 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d773c2e38b6eda4f5b64583f034c4842d91aab13210138f26d4c816435f2050a

Height

#377,851

Difficulty

10.418325

Transactions

5

Size

3.18 KB

Version

2

Bits

0a6b175d

Nonce

93,748

Timestamp

1/27/2014, 10:27:38 AM

Confirmations

6,428,604

Merkle Root

237a7b9873473fba458c58935cb37a9a32d7013d620b83d337503cfa2804b444
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.

2.317 × 10¹⁰⁰(101-digit number)
23171608949481617571…20357575124524216319
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
2.317 × 10¹⁰⁰(101-digit number)
23171608949481617571…20357575124524216319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.634 × 10¹⁰⁰(101-digit number)
46343217898963235143…40715150249048432639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.268 × 10¹⁰⁰(101-digit number)
92686435797926470286…81430300498096865279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.853 × 10¹⁰¹(102-digit number)
18537287159585294057…62860600996193730559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.707 × 10¹⁰¹(102-digit number)
37074574319170588114…25721201992387461119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.414 × 10¹⁰¹(102-digit number)
74149148638341176228…51442403984774922239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.482 × 10¹⁰²(103-digit number)
14829829727668235245…02884807969549844479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.965 × 10¹⁰²(103-digit number)
29659659455336470491…05769615939099688959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.931 × 10¹⁰²(103-digit number)
59319318910672940983…11539231878199377919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.186 × 10¹⁰³(104-digit number)
11863863782134588196…23078463756398755839
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:57,695,731 XPM·at block #6,806,454 · updates every 60s
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