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Block #164,769

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 9:04:23 PM Β· Difficulty 9.8638 Β· 6,631,754 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
76180787bba1a977e2b62b27e72b71e777647953a73bad7f7233afc5dbd73828
View on Chainz β†—

Height

#164,769

Difficulty

9.863787

Transactions

1

Size

200 B

Version

2

Bits

09dd212a

Nonce

164,304

Timestamp

9/14/2013, 9:04:23 PM

Confirmations

6,631,754

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

fd9cb3610cfa9ab9a3f2a469e8f3037fb5e791b52770b821cf56eff54fdb83df
Transactions (1)
Coinbasefd9cb3610cfa9a…56eff54fdb83df
1 in β†’ 1 out10.2600 XPM109 B
AdDUNTYm…v4Zjqa77
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.

1.901 Γ— 10⁹⁢(97-digit number)
19019547178509610528…26022621755322374079
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
1.901 Γ— 10⁹⁢(97-digit number)
19019547178509610528…26022621755322374079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.803 Γ— 10⁹⁢(97-digit number)
38039094357019221057…52045243510644748159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.607 Γ— 10⁹⁢(97-digit number)
76078188714038442114…04090487021289496319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.521 Γ— 10⁹⁷(98-digit number)
15215637742807688422…08180974042578992639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.043 Γ— 10⁹⁷(98-digit number)
30431275485615376845…16361948085157985279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.086 Γ— 10⁹⁷(98-digit number)
60862550971230753691…32723896170315970559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.217 Γ— 10⁹⁸(99-digit number)
12172510194246150738…65447792340631941119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.434 Γ— 10⁹⁸(99-digit number)
24345020388492301476…30895584681263882239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.869 Γ— 10⁹⁸(99-digit number)
48690040776984602953…61791169362527764479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.738 Γ— 10⁹⁸(99-digit number)
97380081553969205906…23582338725055528959
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:57,616,181 XPMΒ·at block #6,796,522 Β· updates every 60s
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