Block #370,178

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/21/2014, 10:01:07 PM · Difficulty 10.4471 · 6,460,422 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2da16071d81f37770866644367aba6f64bd1d66129083d296603bf33b107a7d8

View on Chainz ↗

Height

#370,178

Difficulty

10.447110

Transactions

Size

202 B

Version

Bits

0a7275d4

Nonce

25,315

Timestamp

1/21/2014, 10:01:07 PM

Confirmations

6,460,422

Mined by

⛏️ P2SHASqdfRNpTunqNuXsxMBqCryK9KGfUbuqS8

Merkle Root

a09c680db57e2c75a58639ce8284ddfbfd87b8bb95fb39bb3902922c08a513e6

Transactions (1)

Coinbasea09c680db57e2c…02922c08a513e6

1 in → 1 out9.1500 XPM109 B

ASqdfRNp…GfUbuqS8

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.

2.530 × 10¹⁰¹(102-digit number)

25300638420898935604…33958867429966879999

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.

origin − 1

2.530 × 10¹⁰¹(102-digit number)

25300638420898935604…33958867429966879999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.060 × 10¹⁰¹(102-digit number)

50601276841797871209…67917734859933759999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.012 × 10¹⁰²(103-digit number)

10120255368359574241…35835469719867519999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.024 × 10¹⁰²(103-digit number)

20240510736719148483…71670939439735039999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.048 × 10¹⁰²(103-digit number)

40481021473438296967…43341878879470079999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.096 × 10¹⁰²(103-digit number)

80962042946876593935…86683757758940159999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.619 × 10¹⁰³(104-digit number)

16192408589375318787…73367515517880319999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.238 × 10¹⁰³(104-digit number)

32384817178750637574…46735031035760639999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.476 × 10¹⁰³(104-digit number)

64769634357501275148…93470062071521279999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.295 × 10¹⁰⁴(105-digit number)

12953926871500255029…86940124143042559999

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, …

Cross-reference on Chainz Explorer

Block #370,178

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