Block #453,587

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/21/2014, 10:02:32 AM · Difficulty 10.3859 · 6,371,235 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f612df1efbe12d7780f97868f88566344a0b06cdcd70ffa80b5502ad99267cd6

View on Chainz ↗

Height

#453,587

Difficulty

10.385943

Transactions

Size

901 B

Version

Bits

0a62cd28

Nonce

38,142

Timestamp

3/21/2014, 10:02:32 AM

Confirmations

6,371,235

Mined by

⛏️ aS,AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5922141eb446928aafa6e3f3b2066fb96eceec359e01ecf26e725f3ff6623489

Transactions (1)

Coinbase5922141eb44692…725f3ff6623489

1 in → 22 out9.2600 XPM811 B

AQvZBsUo…hppgRZTJ AScAzqGc…BZ6tV1vJ ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq ATKK7iFz…wZm46KN1

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.

2.559 × 10⁹⁴(95-digit number)

25598729871816851213…57570672153902977919

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

2.559 × 10⁹⁴(95-digit number)

25598729871816851213…57570672153902977919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.119 × 10⁹⁴(95-digit number)

51197459743633702427…15141344307805955839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.023 × 10⁹⁵(96-digit number)

10239491948726740485…30282688615611911679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.047 × 10⁹⁵(96-digit number)

20478983897453480971…60565377231223823359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.095 × 10⁹⁵(96-digit number)

40957967794906961942…21130754462447646719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.191 × 10⁹⁵(96-digit number)

81915935589813923884…42261508924895293439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.638 × 10⁹⁶(97-digit number)

16383187117962784776…84523017849790586879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.276 × 10⁹⁶(97-digit number)

32766374235925569553…69046035699581173759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.553 × 10⁹⁶(97-digit number)

65532748471851139107…38092071399162347519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.310 × 10⁹⁷(98-digit number)

13106549694370227821…76184142798324695039

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 #453,587

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