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Block #1,371,762

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2015, 5:24:57 PM Β· Difficulty 10.8109 Β· 5,467,969 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b070ae60cf410182fe754cc19c4cc4992a369d767c2dcbec4c352ac3b05d627f
View on Chainz β†—

Height

#1,371,762

Difficulty

10.810917

Transactions

1

Size

199 B

Version

2

Bits

0acf9840

Nonce

1,917,411,804

Timestamp

12/16/2015, 5:24:57 PM

Confirmations

5,467,969

Mined by

⛏️ P2SHAU6g5ex8MJSHV6ancM22rzyd4wsXDML7uB

Merkle Root

8bc37d78a4590c408665aaafad1fbcc7d9f268114bf98dc90153158285309164
Transactions (1)
Coinbase8bc37d78a4590c…53158285309164
1 in β†’ 1 out8.5400 XPM110 B
AU6g5ex8…sXDML7uB
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.

4.860 Γ— 10⁹²(93-digit number)
48606641475128976595…72842024409706520309
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
4.860 Γ— 10⁹²(93-digit number)
48606641475128976595…72842024409706520309
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.721 Γ— 10⁹²(93-digit number)
97213282950257953191…45684048819413040619
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.944 Γ— 10⁹³(94-digit number)
19442656590051590638…91368097638826081239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.888 Γ— 10⁹³(94-digit number)
38885313180103181276…82736195277652162479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.777 Γ— 10⁹³(94-digit number)
77770626360206362553…65472390555304324959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.555 Γ— 10⁹⁴(95-digit number)
15554125272041272510…30944781110608649919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.110 Γ— 10⁹⁴(95-digit number)
31108250544082545021…61889562221217299839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.221 Γ— 10⁹⁴(95-digit number)
62216501088165090042…23779124442434599679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.244 Γ— 10⁹⁡(96-digit number)
12443300217633018008…47558248884869199359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.488 Γ— 10⁹⁡(96-digit number)
24886600435266036017…95116497769738398719
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:57,962,133 XPMΒ·at block #6,839,730 Β· updates every 60s
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