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Block #2,249,877

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/13/2017, 4:23:52 PM Β· Difficulty 10.9474 Β· 4,592,480 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
363916d72c02366229c8dc7fdd31fa6819b20e5c50bc5a1c370942cb790e9a4e
View on Chainz β†—

Height

#2,249,877

Difficulty

10.947395

Transactions

2

Size

576 B

Version

2

Bits

0af28879

Nonce

1,988,345,039

Timestamp

8/13/2017, 4:23:52 PM

Confirmations

4,592,480

Mined by

⛏️ P2SHAHH6hvc4wGW7XzCEA8ky6b53nxUuvm5o29

Merkle Root

c12b89d3515b42a5a8e9749dffbda9c76283a7150722a9593ff8311dc00234f5
Transactions (2)
Coinbasea30604051b15b5…f0ed272b9ec69a
1 in β†’ 1 out8.3400 XPM109 B
AHH6hvc4…Uuvm5o29
17880a12edf923…d0f217715b7569
2 in β†’ 2 out738.3105 XPM376 B
ANsKC3h5…ua8f6Gk1AQfjtXq8…MWw1jmja
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.

9.325 Γ— 10⁹⁡(96-digit number)
93255524614600473305…63049974798049933439
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
9.325 Γ— 10⁹⁡(96-digit number)
93255524614600473305…63049974798049933439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.865 Γ— 10⁹⁢(97-digit number)
18651104922920094661…26099949596099866879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.730 Γ— 10⁹⁢(97-digit number)
37302209845840189322…52199899192199733759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.460 Γ— 10⁹⁢(97-digit number)
74604419691680378644…04399798384399467519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁷(98-digit number)
14920883938336075728…08799596768798935039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.984 Γ— 10⁹⁷(98-digit number)
29841767876672151457…17599193537597870079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.968 Γ— 10⁹⁷(98-digit number)
59683535753344302915…35198387075195740159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁸(99-digit number)
11936707150668860583…70396774150391480319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.387 Γ— 10⁹⁸(99-digit number)
23873414301337721166…40793548300782960639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.774 Γ— 10⁹⁸(99-digit number)
47746828602675442332…81587096601565921279
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:57,983,263 XPMΒ·at block #6,842,356 Β· updates every 60s
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