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Block #2,915,801

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/9/2018, 7:40:59 AM Β· Difficulty 11.4449 Β· 3,917,661 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8b35f3ec81b92a46360c3d71452e63d91fd2e0b86ba48c1ce51a7f702dd292da
View on Chainz β†—

Height

#2,915,801

Difficulty

11.444886

Transactions

2

Size

393 B

Version

2

Bits

0b71e40f

Nonce

213,823,549

Timestamp

11/9/2018, 7:40:59 AM

Confirmations

3,917,661

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

e45080a3bdd40b62a19440c802c42576ec1234c7c616361d03632235969d6347
Transactions (2)
Coinbase6715ba020b7016…25b373a0d0d0a2
1 in β†’ 1 out7.6300 XPM110 B
AbXwmGxD…4XXYP765
b7605a60bed163…b3d2c7426c9ca2
1 in β†’ 1 out1122.2773 XPM192 B
AbFieDh2…UG9e4SDN
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.

3.208 Γ— 10⁹⁷(98-digit number)
32088860418213954710…83408181779121845759
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
3.208 Γ— 10⁹⁷(98-digit number)
32088860418213954710…83408181779121845759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.417 Γ— 10⁹⁷(98-digit number)
64177720836427909421…66816363558243691519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.283 Γ— 10⁹⁸(99-digit number)
12835544167285581884…33632727116487383039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.567 Γ— 10⁹⁸(99-digit number)
25671088334571163768…67265454232974766079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.134 Γ— 10⁹⁸(99-digit number)
51342176669142327536…34530908465949532159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.026 Γ— 10⁹⁹(100-digit number)
10268435333828465507…69061816931899064319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.053 Γ— 10⁹⁹(100-digit number)
20536870667656931014…38123633863798128639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.107 Γ— 10⁹⁹(100-digit number)
41073741335313862029…76247267727596257279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.214 Γ— 10⁹⁹(100-digit number)
82147482670627724058…52494535455192514559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.642 Γ— 10¹⁰⁰(101-digit number)
16429496534125544811…04989070910385029119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.285 Γ— 10¹⁰⁰(101-digit number)
32858993068251089623…09978141820770058239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,911,896 XPMΒ·at block #6,833,461 Β· updates every 60s
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