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Block #2,674,204

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/23/2018, 7:21:30 AM Β· Difficulty 11.6997 Β· 4,169,796 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7815553a72635ac848386cae531cee68d70e4d1cdd35e01cad5470975447a4a7
View on Chainz β†—

Height

#2,674,204

Difficulty

11.699716

Transactions

2

Size

1016 B

Version

2

Bits

0bb32099

Nonce

1,813,432,122

Timestamp

5/23/2018, 7:21:30 AM

Confirmations

4,169,796

Mined by

⛏️ P2SHAVU9VW58QEgmbJSBFRYDvg7voNg82uTxJd

Merkle Root

f09cbe36cfaf6e6a297b1f1353b86a07a5efe766eff45c2cf4e929f15efcba72
Transactions (2)
Coinbasef758d35d6ee75e…435a4285e86ba2
1 in β†’ 1 out7.3000 XPM110 B
AVU9VW58…g82uTxJd
4e299815e9e63d…2e32e933e4157e
5 in β†’ 2 out34.1101 XPM816 B
AdFx8dYB…Di8VBb7nAcvsytU5…M4P6Hrcb
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.

2.529 Γ— 10⁹⁴(95-digit number)
25293152867332076440…37186212210360673441
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
2.529 Γ— 10⁹⁴(95-digit number)
25293152867332076440…37186212210360673441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.058 Γ— 10⁹⁴(95-digit number)
50586305734664152881…74372424420721346881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.011 Γ— 10⁹⁡(96-digit number)
10117261146932830576…48744848841442693761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.023 Γ— 10⁹⁡(96-digit number)
20234522293865661152…97489697682885387521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.046 Γ— 10⁹⁡(96-digit number)
40469044587731322305…94979395365770775041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.093 Γ— 10⁹⁡(96-digit number)
80938089175462644610…89958790731541550081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.618 Γ— 10⁹⁢(97-digit number)
16187617835092528922…79917581463083100161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.237 Γ— 10⁹⁢(97-digit number)
32375235670185057844…59835162926166200321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.475 Γ— 10⁹⁢(97-digit number)
64750471340370115688…19670325852332400641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.295 Γ— 10⁹⁷(98-digit number)
12950094268074023137…39340651704664801281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.590 Γ— 10⁹⁷(98-digit number)
25900188536148046275…78681303409329602561
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:57,996,382 XPMΒ·at block #6,843,999 Β· updates every 60s
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