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Block #2,653,116

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2018, 3:24:32 AM Β· Difficulty 11.7405 Β· 4,190,280 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6368fb20d7174f63d1b636368065a7e523e2d3d86032569f3f4edb3e693e9a6f
View on Chainz β†—

Height

#2,653,116

Difficulty

11.740530

Transactions

1

Size

201 B

Version

2

Bits

0bbd9360

Nonce

649,078,253

Timestamp

5/8/2018, 3:24:32 AM

Confirmations

4,190,280

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

e98ba08849ad3b607e412f67ceabde5963362a15fcf6741361ae8704f6189923
Transactions (1)
Coinbasee98ba08849ad3b…ae8704f6189923
1 in β†’ 1 out7.2400 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.056 Γ— 10⁹⁷(98-digit number)
10567869777463101472…73986973670945968641
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
1.056 Γ— 10⁹⁷(98-digit number)
10567869777463101472…73986973670945968641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.113 Γ— 10⁹⁷(98-digit number)
21135739554926202944…47973947341891937281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.227 Γ— 10⁹⁷(98-digit number)
42271479109852405888…95947894683783874561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.454 Γ— 10⁹⁷(98-digit number)
84542958219704811777…91895789367567749121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.690 Γ— 10⁹⁸(99-digit number)
16908591643940962355…83791578735135498241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.381 Γ— 10⁹⁸(99-digit number)
33817183287881924711…67583157470270996481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.763 Γ— 10⁹⁸(99-digit number)
67634366575763849422…35166314940541992961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.352 Γ— 10⁹⁹(100-digit number)
13526873315152769884…70332629881083985921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.705 Γ— 10⁹⁹(100-digit number)
27053746630305539768…40665259762167971841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.410 Γ— 10⁹⁹(100-digit number)
54107493260611079537…81330519524335943681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.082 Γ— 10¹⁰⁰(101-digit number)
10821498652122215907…62661039048671887361
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:57,991,532 XPMΒ·at block #6,843,395 Β· updates every 60s
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