Block #70,661

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/20/2013, 2:47:36 PM · Difficulty 8.9924 · 6,722,386 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a1a5520c7fbc749b8c604fd4bc18f7293b5108550aaea43e6c2b43317a9fb93a

View on Chainz ↗

Height

#70,661

Difficulty

8.992391

Transactions

Size

1.07 KB

Version

Bits

08fe0d4f

Nonce

689

Timestamp

7/20/2013, 2:47:36 PM

Confirmations

6,722,386

Merkle Root

512f34cdb6a5a0165c8e759b2bf3abbc437f275bd76c57f077962ecc44fb68f5

Transactions (3)

Coinbase2f3290ab97f72f…b192ee82f48574

1 in → 1 out12.3700 XPM110 B

AZDgU5ry…dmcwdqVC

bb86741e7864eb…4362f619832f1b

2 in → 2 out10.0300 XPM374 B

AWT9hCSF…8w3t7Tzk Ae9xrbKt…TJDD2D5P

ee070da04fa2cd…e0e73c7f9f9031

3 in → 2 out3.1342 XPM522 B

ANGjaARV…JuAz8bA4 AL4cfuvB…cvRLdJC8

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.

4.826 × 10⁹⁷(98-digit number)

48263617011217713295…96346814991108609519

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

4.826 × 10⁹⁷(98-digit number)

48263617011217713295…96346814991108609519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.652 × 10⁹⁷(98-digit number)

96527234022435426590…92693629982217219039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.930 × 10⁹⁸(99-digit number)

19305446804487085318…85387259964434438079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.861 × 10⁹⁸(99-digit number)

38610893608974170636…70774519928868876159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.722 × 10⁹⁸(99-digit number)

77221787217948341272…41549039857737752319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.544 × 10⁹⁹(100-digit number)

15444357443589668254…83098079715475504639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.088 × 10⁹⁹(100-digit number)

30888714887179336509…66196159430951009279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.177 × 10⁹⁹(100-digit number)

61777429774358673018…32392318861902018559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.235 × 10¹⁰⁰(101-digit number)

12355485954871734603…64784637723804037119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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