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Block #1,613,849

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/4/2016, 2:58:21 PM Β· Difficulty 10.5952 Β· 5,227,656 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d6b3534bc168e0d128b5d72fe08d8e8c010488c1dfc8f781c403960da96e88e
View on Chainz β†—

Height

#1,613,849

Difficulty

10.595201

Transactions

1

Size

199 B

Version

2

Bits

0a985f18

Nonce

86,867,738

Timestamp

6/4/2016, 2:58:21 PM

Confirmations

5,227,656

Mined by

⛏️ P2SHAcDh7Li3BzJt8Zr7wargWTFfWKPeRSzTaL

Merkle Root

e98340559d70526c944034a1d715646919ef2772b237ea01d6c0b89e4fae8049
Transactions (1)
Coinbasee98340559d7052…c0b89e4fae8049
1 in β†’ 1 out8.8900 XPM109 B
AcDh7Li3…PeRSzTaL
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.

5.674 Γ— 10⁹³(94-digit number)
56749275452790549623…84755929169639307989
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
5.674 Γ— 10⁹³(94-digit number)
56749275452790549623…84755929169639307989
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.134 Γ— 10⁹⁴(95-digit number)
11349855090558109924…69511858339278615979
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.269 Γ— 10⁹⁴(95-digit number)
22699710181116219849…39023716678557231959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.539 Γ— 10⁹⁴(95-digit number)
45399420362232439699…78047433357114463919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.079 Γ— 10⁹⁴(95-digit number)
90798840724464879398…56094866714228927839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.815 Γ— 10⁹⁡(96-digit number)
18159768144892975879…12189733428457855679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.631 Γ— 10⁹⁡(96-digit number)
36319536289785951759…24379466856915711359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.263 Γ— 10⁹⁡(96-digit number)
72639072579571903518…48758933713831422719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.452 Γ— 10⁹⁢(97-digit number)
14527814515914380703…97517867427662845439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.905 Γ— 10⁹⁢(97-digit number)
29055629031828761407…95035734855325690879
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:57,976,419 XPMΒ·at block #6,841,504 Β· updates every 60s
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