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Block #3,154,147

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/25/2019, 1:29:09 AM Β· Difficulty 11.3164 Β· 3,683,976 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7ed497e1b2cac04aa524d0ee45251d12807be04931099d5bd1f918afabbb28d3
View on Chainz β†—

Height

#3,154,147

Difficulty

11.316353

Transactions

2

Size

1.72 KB

Version

2

Bits

0b50fc88

Nonce

1,644,937,085

Timestamp

4/25/2019, 1:29:09 AM

Confirmations

3,683,976

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

c578cc9067dd9c8bcb97938885fcaf082bc331b3742b71a4dd8ffe7f1c40f234
Transactions (2)
Coinbase3b7402d0503049…229f0d35b0a6d2
1 in β†’ 1 out7.8300 XPM110 B
AbXwmGxD…4XXYP765
c3154af7543c67…0ebfdb2fb9c460
10 in β†’ 2 out2470.4317 XPM1.52 KB
Ab9ymyu2…yh7Uu4SLARkrfHMm…2tugX2Ei
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.

2.728 Γ— 10⁹³(94-digit number)
27287942506885117287…73092133449770967041
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.728 Γ— 10⁹³(94-digit number)
27287942506885117287…73092133449770967041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.457 Γ— 10⁹³(94-digit number)
54575885013770234574…46184266899541934081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.091 Γ— 10⁹⁴(95-digit number)
10915177002754046914…92368533799083868161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.183 Γ— 10⁹⁴(95-digit number)
21830354005508093829…84737067598167736321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.366 Γ— 10⁹⁴(95-digit number)
43660708011016187659…69474135196335472641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.732 Γ— 10⁹⁴(95-digit number)
87321416022032375319…38948270392670945281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.746 Γ— 10⁹⁡(96-digit number)
17464283204406475063…77896540785341890561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.492 Γ— 10⁹⁡(96-digit number)
34928566408812950127…55793081570683781121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.985 Γ— 10⁹⁡(96-digit number)
69857132817625900255…11586163141367562241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.397 Γ— 10⁹⁢(97-digit number)
13971426563525180051…23172326282735124481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.794 Γ— 10⁹⁢(97-digit number)
27942853127050360102…46344652565470248961
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,949,340 XPMΒ·at block #6,838,122 Β· updates every 60s
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