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Block #989,916

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/25/2015, 9:12:18 AM Β· Difficulty 10.8521 Β· 5,813,598 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
838c66656f25e1e2b09f14c302150fecb2ec14587d9ecdc85c280e2b6b7e655e
View on Chainz β†—

Height

#989,916

Difficulty

10.852096

Transactions

1

Size

199 B

Version

2

Bits

0ada22f9

Nonce

506,522,279

Timestamp

3/25/2015, 9:12:18 AM

Confirmations

5,813,598

Mined by

⛏️ P2SHANvWdJZ1NsTLaTE5Q1g43kN3SLTuXdvdy6

Merkle Root

e0015b3cbc279850051fa5f03bd1ed48d2db849c37b438a6a1e6f35d72517099
Transactions (1)
Coinbasee0015b3cbc2798…e6f35d72517099
1 in β†’ 1 out8.4800 XPM109 B
ANvWdJZ1…TuXdvdy6
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.

3.394 Γ— 10⁹⁴(95-digit number)
33940830960891521019…76978499498218924701
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
3.394 Γ— 10⁹⁴(95-digit number)
33940830960891521019…76978499498218924701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.788 Γ— 10⁹⁴(95-digit number)
67881661921783042038…53956998996437849401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.357 Γ— 10⁹⁡(96-digit number)
13576332384356608407…07913997992875698801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.715 Γ— 10⁹⁡(96-digit number)
27152664768713216815…15827995985751397601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.430 Γ— 10⁹⁡(96-digit number)
54305329537426433630…31655991971502795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.086 Γ— 10⁹⁢(97-digit number)
10861065907485286726…63311983943005590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.172 Γ— 10⁹⁢(97-digit number)
21722131814970573452…26623967886011180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.344 Γ— 10⁹⁢(97-digit number)
43444263629941146904…53247935772022361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.688 Γ— 10⁹⁢(97-digit number)
86888527259882293808…06495871544044723201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.737 Γ— 10⁹⁷(98-digit number)
17377705451976458761…12991743088089446401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,672,137 XPMΒ·at block #6,803,513 Β· updates every 60s
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