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Block #496,978

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/17/2014, 8:58:36 AM Β· Difficulty 10.7614 Β· 6,317,256 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6eacd5c4017a3752b00a012c8855f35a06ad098f44cf2c4635456f10d52818f8
View on Chainz β†—

Height

#496,978

Difficulty

10.761352

Transactions

1

Size

205 B

Version

2

Bits

0ac2e7f3

Nonce

45,092

Timestamp

4/17/2014, 8:58:36 AM

Confirmations

6,317,256

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

bbe96bea4753019d7e9d51f42495c416f69aa3344f52b21b43366edac675cf6e
Transactions (1)
Coinbasebbe96bea475301…366edac675cf6e
1 in β†’ 1 out8.6200 XPM116 B
AbwWkWZt…kawDhufa
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.

1.411 Γ— 10⁹³(94-digit number)
14110490542722165119…48196965398958899199
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.411 Γ— 10⁹³(94-digit number)
14110490542722165119…48196965398958899199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.822 Γ— 10⁹³(94-digit number)
28220981085444330238…96393930797917798399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.644 Γ— 10⁹³(94-digit number)
56441962170888660476…92787861595835596799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.128 Γ— 10⁹⁴(95-digit number)
11288392434177732095…85575723191671193599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.257 Γ— 10⁹⁴(95-digit number)
22576784868355464190…71151446383342387199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.515 Γ— 10⁹⁴(95-digit number)
45153569736710928380…42302892766684774399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.030 Γ— 10⁹⁴(95-digit number)
90307139473421856761…84605785533369548799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.806 Γ— 10⁹⁡(96-digit number)
18061427894684371352…69211571066739097599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.612 Γ— 10⁹⁡(96-digit number)
36122855789368742704…38423142133478195199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.224 Γ— 10⁹⁡(96-digit number)
72245711578737485409…76846284266956390399
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,757,943 XPMΒ·at block #6,814,233 Β· updates every 60s
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