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Block #2,642,484

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 6:17:12 PM Β· Difficulty 11.6540 Β· 4,194,169 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c6c6c072164e3e1b3b5a4190a7b7cb89768915aaf1a9cd7094ad8ef3f9fca1f
View on Chainz β†—

Height

#2,642,484

Difficulty

11.653975

Transactions

1

Size

200 B

Version

2

Bits

0ba76ae1

Nonce

638,072,010

Timestamp

5/1/2018, 6:17:12 PM

Confirmations

4,194,169

Mined by

⛏️ P2SHAXDmLRrZ9jE4BvxyVF9gbPaF6RqCTYWcus

Merkle Root

c24d6967ccf2306707fab3b8c610049b6ee282d9e6cb87d85d83dbb0ffbe2175
Transactions (1)
Coinbasec24d6967ccf230…83dbb0ffbe2175
1 in β†’ 1 out7.3500 XPM110 B
AXDmLRrZ…qCTYWcus
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.

1.549 Γ— 10⁹⁡(96-digit number)
15496603065060266573…25572690795190829921
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
1.549 Γ— 10⁹⁡(96-digit number)
15496603065060266573…25572690795190829921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.099 Γ— 10⁹⁡(96-digit number)
30993206130120533146…51145381590381659841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.198 Γ— 10⁹⁡(96-digit number)
61986412260241066292…02290763180763319681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.239 Γ— 10⁹⁢(97-digit number)
12397282452048213258…04581526361526639361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.479 Γ— 10⁹⁢(97-digit number)
24794564904096426517…09163052723053278721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.958 Γ— 10⁹⁢(97-digit number)
49589129808192853034…18326105446106557441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.917 Γ— 10⁹⁢(97-digit number)
99178259616385706068…36652210892213114881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.983 Γ— 10⁹⁷(98-digit number)
19835651923277141213…73304421784426229761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.967 Γ— 10⁹⁷(98-digit number)
39671303846554282427…46608843568852459521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.934 Γ— 10⁹⁷(98-digit number)
79342607693108564854…93217687137704919041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.586 Γ— 10⁹⁸(99-digit number)
15868521538621712970…86435374275409838081
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:57,937,499 XPMΒ·at block #6,836,652 Β· updates every 60s
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