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Block #2,051,421

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 12:33:46 PM Β· Difficulty 10.7136 Β· 4,789,041 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e6f3312297b8dc9f3ac1bd388e6a5bd24493a493c7003d026b3bc0c390e0d499
View on Chainz β†—

Height

#2,051,421

Difficulty

10.713615

Transactions

1

Size

200 B

Version

2

Bits

0ab6af7e

Nonce

39,824,214

Timestamp

4/3/2017, 12:33:46 PM

Confirmations

4,789,041

Mined by

⛏️ P2SHAdtom3bYBbRbmv9Y4QNSQgrkXjZQGGhVr8

Merkle Root

a2d268ddfe7b71d93ed3e34c06682af4e1f33b24c9a2103f3a5cf3619476defa
Transactions (1)
Coinbasea2d268ddfe7b71…5cf3619476defa
1 in β†’ 1 out8.7000 XPM110 B
Adtom3bY…ZQGGhVr8
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.

3.688 Γ— 10⁹³(94-digit number)
36887168216638947925…63308018595906696399
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
3.688 Γ— 10⁹³(94-digit number)
36887168216638947925…63308018595906696399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.377 Γ— 10⁹³(94-digit number)
73774336433277895851…26616037191813392799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.475 Γ— 10⁹⁴(95-digit number)
14754867286655579170…53232074383626785599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.950 Γ— 10⁹⁴(95-digit number)
29509734573311158340…06464148767253571199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.901 Γ— 10⁹⁴(95-digit number)
59019469146622316680…12928297534507142399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁡(96-digit number)
11803893829324463336…25856595069014284799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.360 Γ— 10⁹⁡(96-digit number)
23607787658648926672…51713190138028569599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.721 Γ— 10⁹⁡(96-digit number)
47215575317297853344…03426380276057139199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.443 Γ— 10⁹⁡(96-digit number)
94431150634595706689…06852760552114278399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.888 Γ— 10⁹⁢(97-digit number)
18886230126919141337…13705521104228556799
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:57,968,024 XPMΒ·at block #6,840,461 Β· updates every 60s
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