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Block #2,679,695

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/27/2018, 4:52:30 AM Β· Difficulty 11.6926 Β· 4,161,462 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bb6d9177445af974fe41fb60cf03c4306e239bd40cd570cd5d3c9db91b6fc8ee
View on Chainz β†—

Height

#2,679,695

Difficulty

11.692599

Transactions

1

Size

200 B

Version

2

Bits

0bb14e2d

Nonce

459,079,832

Timestamp

5/27/2018, 4:52:30 AM

Confirmations

4,161,462

Mined by

⛏️ P2SHAPDgcJ8crjuyAoPWQtwrNT6gvQenSeumwi

Merkle Root

8ca96cf3014abc5fb262d89b15dbfbece3b29725402f5ca0f5e80968d7535630
Transactions (1)
Coinbase8ca96cf3014abc…e80968d7535630
1 in β†’ 1 out7.3000 XPM110 B
APDgcJ8c…enSeumwi
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.

9.368 Γ— 10⁹³(94-digit number)
93689606337571507749…32801368530891031061
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
9.368 Γ— 10⁹³(94-digit number)
93689606337571507749…32801368530891031061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.873 Γ— 10⁹⁴(95-digit number)
18737921267514301549…65602737061782062121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.747 Γ— 10⁹⁴(95-digit number)
37475842535028603099…31205474123564124241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.495 Γ— 10⁹⁴(95-digit number)
74951685070057206199…62410948247128248481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.499 Γ— 10⁹⁡(96-digit number)
14990337014011441239…24821896494256496961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.998 Γ— 10⁹⁡(96-digit number)
29980674028022882479…49643792988512993921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.996 Γ— 10⁹⁡(96-digit number)
59961348056045764959…99287585977025987841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.199 Γ— 10⁹⁢(97-digit number)
11992269611209152991…98575171954051975681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.398 Γ— 10⁹⁢(97-digit number)
23984539222418305983…97150343908103951361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.796 Γ— 10⁹⁢(97-digit number)
47969078444836611967…94300687816207902721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.593 Γ— 10⁹⁢(97-digit number)
95938156889673223935…88601375632415805441
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:57,973,620 XPMΒ·at block #6,841,156 Β· updates every 60s
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