Block #569,857

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/31/2014, 10:48:07 AM · Difficulty 10.9647 · 6,232,547 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0a9737cddbe97b2e8a5ca2d56c2fd2676f68f3d950449ac092718ff117dd4ea3

View on Chainz ↗

Height

#569,857

Difficulty

10.964671

Transactions

Size

1.23 KB

Version

Bits

0af6f4ae

Nonce

320,837,924

Timestamp

5/31/2014, 10:48:07 AM

Confirmations

6,232,547

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bb6f77184cb5b84a90875b62b829b1685f146268d94bb4104bb11536c3b789d8

Transactions (5)

Coinbase79e924da89d02f…79d4c8fc262c9a

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

86c35f2929b938…3c0d5c8b811074

2 in → 2 out15.5119 XPM375 B

AGkJKXdc…NadHPcjY AN5egmZF…vjXqiPGT

0c2e541d806a18…c65beb6ccbd5ff

1 in → 2 out7.2799 XPM226 B

AS9ZCvju…bu3NEFwZ AboggwzU…itjMXpQj

926eabaccf2eed…35dd71d3d6a021

1 in → 2 out7.7784 XPM226 B

AKtM9WEm…o9EQAsSn AcVexCzF…SY75pd2v

f2e4d7fcb2f56c…f1a6116153dd16

1 in → 2 out7.2634 XPM226 B

AGdWVjRk…LFVsqCnK AFn5v1Sg…ctgYs8nH

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.

2.871 × 10⁹⁸(99-digit number)

28714347340639866329…66593677311424330399

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

2.871 × 10⁹⁸(99-digit number)

28714347340639866329…66593677311424330399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.742 × 10⁹⁸(99-digit number)

57428694681279732659…33187354622848660799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.148 × 10⁹⁹(100-digit number)

11485738936255946531…66374709245697321599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.297 × 10⁹⁹(100-digit number)

22971477872511893063…32749418491394643199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.594 × 10⁹⁹(100-digit number)

45942955745023786127…65498836982789286399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.188 × 10⁹⁹(100-digit number)

91885911490047572255…30997673965578572799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.837 × 10¹⁰⁰(101-digit number)

18377182298009514451…61995347931157145599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.675 × 10¹⁰⁰(101-digit number)

36754364596019028902…23990695862314291199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.350 × 10¹⁰⁰(101-digit number)

73508729192038057804…47981391724628582399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.470 × 10¹⁰¹(102-digit number)

14701745838407611560…95962783449257164799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.940 × 10¹⁰¹(102-digit number)

29403491676815223121…91925566898514329599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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