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Block #240,464

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/2/2013, 3:34:14 PM Β· Difficulty 9.9566 Β· 6,563,203 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d61e5df06a937780124c4b8cf9bf011266dd4a9dee3279b9ea4fe4417b307dc2
View on Chainz β†—

Height

#240,464

Difficulty

9.956634

Transactions

1

Size

197 B

Version

2

Bits

09f4e5ef

Nonce

8,065

Timestamp

11/2/2013, 3:34:14 PM

Confirmations

6,563,203

Mined by

⛏️ P2SHASUtGRx8bDVJURUf8WLJkL5tX6vh2tTKJs

Merkle Root

776bcbc2ac5a2b56b86cba7d1979d13519aec9c6804b43e84cefa4882d1e66d4
Transactions (1)
Coinbase776bcbc2ac5a2b…efa4882d1e66d4
1 in β†’ 1 out10.0700 XPM109 B
ASUtGRx8…vh2tTKJs
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.

1.548 Γ— 10⁹⁰(91-digit number)
15484590425835665426…26522586956000838239
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
1.548 Γ— 10⁹⁰(91-digit number)
15484590425835665426…26522586956000838239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.096 Γ— 10⁹⁰(91-digit number)
30969180851671330853…53045173912001676479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.193 Γ— 10⁹⁰(91-digit number)
61938361703342661707…06090347824003352959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.238 Γ— 10⁹¹(92-digit number)
12387672340668532341…12180695648006705919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.477 Γ— 10⁹¹(92-digit number)
24775344681337064682…24361391296013411839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.955 Γ— 10⁹¹(92-digit number)
49550689362674129365…48722782592026823679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.910 Γ— 10⁹¹(92-digit number)
99101378725348258731…97445565184053647359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.982 Γ— 10⁹²(93-digit number)
19820275745069651746…94891130368107294719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.964 Γ— 10⁹²(93-digit number)
39640551490139303492…89782260736214589439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.928 Γ— 10⁹²(93-digit number)
79281102980278606985…79564521472429178879
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,673,372 XPMΒ·at block #6,803,666 Β· updates every 60s
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