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Block #1,371,778

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2015, 5:49:09 PM Β· Difficulty 10.8106 Β· 5,470,023 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0e275efb0c4f46f9893ca2ddc90989c8170d0652b8b4a8ddeb0ce3c709dc3a5e
View on Chainz β†—

Height

#1,371,778

Difficulty

10.810592

Transactions

1

Size

200 B

Version

2

Bits

0acf82f7

Nonce

1,205,904,107

Timestamp

12/16/2015, 5:49:09 PM

Confirmations

5,470,023

Mined by

⛏️ P2SHAd7yxFMaWXGVr3ENk4VJHnsTnmkNt9mPbw

Merkle Root

a3576f2a93c6a2f3b0994280dcc3bb6add1ddd46220b9a9fedafb2eb666e674b
Transactions (1)
Coinbasea3576f2a93c6a2…afb2eb666e674b
1 in β†’ 1 out8.5400 XPM110 B
Ad7yxFMa…kNt9mPbw
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.

1.140 Γ— 10⁹⁡(96-digit number)
11400012797973237190…70990989597511529419
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
1.140 Γ— 10⁹⁡(96-digit number)
11400012797973237190…70990989597511529419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.280 Γ— 10⁹⁡(96-digit number)
22800025595946474381…41981979195023058839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.560 Γ— 10⁹⁡(96-digit number)
45600051191892948762…83963958390046117679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.120 Γ— 10⁹⁡(96-digit number)
91200102383785897525…67927916780092235359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.824 Γ— 10⁹⁢(97-digit number)
18240020476757179505…35855833560184470719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.648 Γ— 10⁹⁢(97-digit number)
36480040953514359010…71711667120368941439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.296 Γ— 10⁹⁢(97-digit number)
72960081907028718020…43423334240737882879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.459 Γ— 10⁹⁷(98-digit number)
14592016381405743604…86846668481475765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.918 Γ— 10⁹⁷(98-digit number)
29184032762811487208…73693336962951531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.836 Γ— 10⁹⁷(98-digit number)
58368065525622974416…47386673925903063039
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:57,978,787 XPMΒ·at block #6,841,800 Β· updates every 60s
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