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Block #2,287,328

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2017, 4:27:23 AM Β· Difficulty 10.9555 Β· 4,549,243 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a3563757712f2d8109c8196821a74d7e9f17c035f3c13679b03ead0dcbe3bbcb
View on Chainz β†—

Height

#2,287,328

Difficulty

10.955538

Transactions

1

Size

200 B

Version

2

Bits

0af49e20

Nonce

403,755,762

Timestamp

9/8/2017, 4:27:23 AM

Confirmations

4,549,243

Mined by

⛏️ P2SHAYsJ7JpvujRNmTnzeuHbATcQezEP3i53NM

Merkle Root

a61f8481a8a732c7dc8c1c742d20eed4cc1f6e9e42ba95e34b722f3c4896b4b1
Transactions (1)
Coinbasea61f8481a8a732…722f3c4896b4b1
1 in β†’ 1 out8.3200 XPM109 B
AYsJ7Jpv…EP3i53NM
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.

1.508 Γ— 10⁹⁢(97-digit number)
15088590115574369110…17185779528762969599
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
1.508 Γ— 10⁹⁢(97-digit number)
15088590115574369110…17185779528762969599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.017 Γ— 10⁹⁢(97-digit number)
30177180231148738220…34371559057525939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.035 Γ— 10⁹⁢(97-digit number)
60354360462297476440…68743118115051878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.207 Γ— 10⁹⁷(98-digit number)
12070872092459495288…37486236230103756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.414 Γ— 10⁹⁷(98-digit number)
24141744184918990576…74972472460207513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.828 Γ— 10⁹⁷(98-digit number)
48283488369837981152…49944944920415027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.656 Γ— 10⁹⁷(98-digit number)
96566976739675962305…99889889840830054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.931 Γ— 10⁹⁸(99-digit number)
19313395347935192461…99779779681660108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.862 Γ— 10⁹⁸(99-digit number)
38626790695870384922…99559559363320217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.725 Γ— 10⁹⁸(99-digit number)
77253581391740769844…99119118726640435199
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:57,936,833 XPMΒ·at block #6,836,570 Β· updates every 60s
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