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Block #2,757,342

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2018, 10:59:29 AM Β· Difficulty 11.6646 Β· 4,085,137 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dea022e8cb53cd4ad7cb10e8fd9d5f84c3df17f5e8de8338995912f96f0eee50
View on Chainz β†—

Height

#2,757,342

Difficulty

11.664635

Transactions

2

Size

1.43 KB

Version

2

Bits

0baa257e

Nonce

678,825,197

Timestamp

7/20/2018, 10:59:29 AM

Confirmations

4,085,137

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

b14e36e81b602261787a1238310d93f53ede67611fc42cde48acdd75d6b34e87
Transactions (2)
Coinbase69af103865f937…20a28f4515e1c6
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
c559aaf69084b7…7247f2ec41546e
8 in β†’ 2 out112.9246 XPM1.23 KB
AQmjqzoU…5U6sbve9AMAE5bno…UkpmeKb9
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.

1.463 Γ— 10⁹⁴(95-digit number)
14633696764091963038…27535037304508723901
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
1.463 Γ— 10⁹⁴(95-digit number)
14633696764091963038…27535037304508723901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.926 Γ— 10⁹⁴(95-digit number)
29267393528183926076…55070074609017447801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.853 Γ— 10⁹⁴(95-digit number)
58534787056367852152…10140149218034895601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.170 Γ— 10⁹⁡(96-digit number)
11706957411273570430…20280298436069791201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.341 Γ— 10⁹⁡(96-digit number)
23413914822547140861…40560596872139582401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.682 Γ— 10⁹⁡(96-digit number)
46827829645094281722…81121193744279164801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.365 Γ— 10⁹⁡(96-digit number)
93655659290188563444…62242387488558329601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.873 Γ— 10⁹⁢(97-digit number)
18731131858037712688…24484774977116659201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.746 Γ— 10⁹⁢(97-digit number)
37462263716075425377…48969549954233318401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.492 Γ— 10⁹⁢(97-digit number)
74924527432150850755…97939099908466636801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.498 Γ— 10⁹⁷(98-digit number)
14984905486430170151…95878199816933273601
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:57,984,250 XPMΒ·at block #6,842,478 Β· updates every 60s
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