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Block #151,452

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2013, 4:50:28 PM Β· Difficulty 9.8604 Β· 6,665,075 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c9cc9a816f9b92dd70954f1ae8e3258d4ef1d065cc7878e12ce6eea8d0bd2352
View on Chainz β†—

Height

#151,452

Difficulty

9.860423

Transactions

1

Size

198 B

Version

2

Bits

09dc44a7

Nonce

29,363

Timestamp

9/5/2013, 4:50:28 PM

Confirmations

6,665,075

Mined by

⛏️ P2SHAXEBNNcSm6Wm5hSxS8f83hjqS74FopSeij

Merkle Root

6f2cd3af07e936f3cd3574a9e060f601842b232eb089763c9256e380e9965c5e
Transactions (1)
Coinbase6f2cd3af07e936…56e380e9965c5e
1 in β†’ 1 out10.2700 XPM109 B
AXEBNNcS…4FopSeij
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.379 Γ— 10⁹²(93-digit number)
63797784278455356015…52623790908039146319
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.379 Γ— 10⁹²(93-digit number)
63797784278455356015…52623790908039146319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.275 Γ— 10⁹³(94-digit number)
12759556855691071203…05247581816078292639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.551 Γ— 10⁹³(94-digit number)
25519113711382142406…10495163632156585279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.103 Γ— 10⁹³(94-digit number)
51038227422764284812…20990327264313170559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.020 Γ— 10⁹⁴(95-digit number)
10207645484552856962…41980654528626341119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.041 Γ— 10⁹⁴(95-digit number)
20415290969105713924…83961309057252682239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.083 Γ— 10⁹⁴(95-digit number)
40830581938211427849…67922618114505364479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.166 Γ— 10⁹⁴(95-digit number)
81661163876422855699…35845236229010728959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.633 Γ— 10⁹⁡(96-digit number)
16332232775284571139…71690472458021457919
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,776,342 XPMΒ·at block #6,816,526 Β· updates every 60s
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