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Block #2,083,153

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/22/2017, 7:15:30 PM Β· Difficulty 10.8708 Β· 4,743,955 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
75f87b5c9dfe36d89b92bc86bdb4a487beb81b51e23cfc2d8614e626447e3094
View on Chainz β†—

Height

#2,083,153

Difficulty

10.870797

Transactions

2

Size

721 B

Version

2

Bits

0adeec93

Nonce

897,865,438

Timestamp

4/22/2017, 7:15:30 PM

Confirmations

4,743,955

Mined by

⛏️ P2SHAX65AcyAcWGRXKcvBhjwnezncWzt9mPb88

Merkle Root

206801c1ab3dbf10dbd06dbeb8e2d39f431e5071c3efe99916895e28af8a38ad
Transactions (2)
Coinbase1084003e1f8804…2d4365e80ff9f8
1 in β†’ 1 out8.4600 XPM110 B
AX65AcyA…zt9mPb88
135319da3adc32…ca3900245690f6
3 in β†’ 2 out363.8000 XPM521 B
AXo7xgdi…w5m2AWXoALS8deFq…L9XLhDT7
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.

7.161 Γ— 10⁹⁴(95-digit number)
71611970363044500546…71170022322185756999
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
7.161 Γ— 10⁹⁴(95-digit number)
71611970363044500546…71170022322185756999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.432 Γ— 10⁹⁡(96-digit number)
14322394072608900109…42340044644371513999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.864 Γ— 10⁹⁡(96-digit number)
28644788145217800218…84680089288743027999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.728 Γ— 10⁹⁡(96-digit number)
57289576290435600437…69360178577486055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.145 Γ— 10⁹⁢(97-digit number)
11457915258087120087…38720357154972111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.291 Γ— 10⁹⁢(97-digit number)
22915830516174240174…77440714309944223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.583 Γ— 10⁹⁢(97-digit number)
45831661032348480349…54881428619888447999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.166 Γ— 10⁹⁢(97-digit number)
91663322064696960699…09762857239776895999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.833 Γ— 10⁹⁷(98-digit number)
18332664412939392139…19525714479553791999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.666 Γ— 10⁹⁷(98-digit number)
36665328825878784279…39051428959107583999
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:57,861,042 XPMΒ·at block #6,827,107 Β· updates every 60s
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