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Block #1,216,817

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/1/2015, 7:54:54 AM Β· Difficulty 10.7248 Β· 5,627,586 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0f32df398066c4e6311c8b0713e2b99b6270334a8156a6fc85e48ca82e179ac5
View on Chainz β†—

Height

#1,216,817

Difficulty

10.724814

Transactions

2

Size

1.43 KB

Version

2

Bits

0ab98d61

Nonce

96,872,094

Timestamp

9/1/2015, 7:54:54 AM

Confirmations

5,627,586

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

5206f68f934243f6f175fdd4637c19b112d4a1560205cc4d1f7a6b97e6c4fc8f
Transactions (2)
Coinbase648766c0598022…456badfdd44d75
1 in β†’ 1 out8.7200 XPM116 B
AJCEY9yy…tg97E6zm
9a74b9e2aae584…649bc4f9054311
8 in β†’ 2 out50000.0100 XPM1.23 KB
AYKArr5V…V9VqiqCZAHWvCaLW…pRi2Yd1i
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.

7.304 Γ— 10⁹⁴(95-digit number)
73043598037240382403…95649028633566660549
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
7.304 Γ— 10⁹⁴(95-digit number)
73043598037240382403…95649028633566660549
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.460 Γ— 10⁹⁡(96-digit number)
14608719607448076480…91298057267133321099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.921 Γ— 10⁹⁡(96-digit number)
29217439214896152961…82596114534266642199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.843 Γ— 10⁹⁡(96-digit number)
58434878429792305922…65192229068533284399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁢(97-digit number)
11686975685958461184…30384458137066568799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.337 Γ— 10⁹⁢(97-digit number)
23373951371916922369…60768916274133137599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.674 Γ— 10⁹⁢(97-digit number)
46747902743833844738…21537832548266275199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.349 Γ— 10⁹⁢(97-digit number)
93495805487667689476…43075665096532550399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.869 Γ— 10⁹⁷(98-digit number)
18699161097533537895…86151330193065100799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.739 Γ— 10⁹⁷(98-digit number)
37398322195067075790…72302660386130201599
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:57,999,616 XPMΒ·at block #6,844,402 Β· updates every 60s
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