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Block #2,648,046

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 6:25:58 AM Β· Difficulty 11.7653 Β· 4,184,538 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab03708fe57d7197e610ef3f0037c0ae6245b70579b7c56e50fd14cb6780f5b3
View on Chainz β†—

Height

#2,648,046

Difficulty

11.765316

Transactions

2

Size

4.32 KB

Version

2

Bits

0bc3ebb8

Nonce

1,426,453,479

Timestamp

5/4/2018, 6:25:58 AM

Confirmations

4,184,538

Mined by

⛏️ P2SHATwuYDXq3UMReHcmBNjPUxbhj3g3rzRUkd

Merkle Root

b1e3b32347e08bee6441d0f8d86764e80cdd8bd3effb8122c9cd4da1bcce28e0
Transactions (2)
Coinbaseaed4a5e6d076a4…4e9edd5332f607
1 in β†’ 1 out7.2600 XPM110 B
ATwuYDXq…g3rzRUkd
63f075cdbd3469…7c9f769500952e
28 in β†’ 2 out136.8652 XPM4.12 KB
AHPjYoGG…7KPWQ2xTAb72jjeS…y7jhVcYk
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.

5.399 Γ— 10⁹⁡(96-digit number)
53997622687572632090…67184037268105197439
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
5.399 Γ— 10⁹⁡(96-digit number)
53997622687572632090…67184037268105197439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.079 Γ— 10⁹⁢(97-digit number)
10799524537514526418…34368074536210394879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.159 Γ— 10⁹⁢(97-digit number)
21599049075029052836…68736149072420789759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.319 Γ— 10⁹⁢(97-digit number)
43198098150058105672…37472298144841579519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.639 Γ— 10⁹⁢(97-digit number)
86396196300116211345…74944596289683159039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.727 Γ— 10⁹⁷(98-digit number)
17279239260023242269…49889192579366318079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.455 Γ— 10⁹⁷(98-digit number)
34558478520046484538…99778385158732636159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.911 Γ— 10⁹⁷(98-digit number)
69116957040092969076…99556770317465272319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁸(99-digit number)
13823391408018593815…99113540634930544639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.764 Γ— 10⁹⁸(99-digit number)
27646782816037187630…98227081269861089279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.529 Γ— 10⁹⁸(99-digit number)
55293565632074375261…96454162539722178559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.105 Γ— 10⁹⁹(100-digit number)
11058713126414875052…92908325079444357119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,904,820 XPMΒ·at block #6,832,583 Β· updates every 60s
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