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Block #711,244

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/7/2014, 6:12:38 PM Β· Difficulty 10.9560 Β· 6,102,898 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
73598fdde69b846ccd040559bb4926a8fdeae63e2c495cd7541c42e50ab91182
View on Chainz β†—

Height

#711,244

Difficulty

10.956044

Transactions

1

Size

206 B

Version

2

Bits

0af4bf4b

Nonce

2,013,512,343

Timestamp

9/7/2014, 6:12:38 PM

Confirmations

6,102,898

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

315f8f8e91a5157dbf26b0e021d0f5ade7ce9ca320783b65bb9213d1df6cd52d
Transactions (1)
Coinbase315f8f8e91a515…9213d1df6cd52d
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.225 Γ— 10⁹⁡(96-digit number)
12256062174923223449…07076923788162656079
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
1.225 Γ— 10⁹⁡(96-digit number)
12256062174923223449…07076923788162656079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.451 Γ— 10⁹⁡(96-digit number)
24512124349846446899…14153847576325312159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.902 Γ— 10⁹⁡(96-digit number)
49024248699692893799…28307695152650624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.804 Γ— 10⁹⁡(96-digit number)
98048497399385787599…56615390305301248639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.960 Γ— 10⁹⁢(97-digit number)
19609699479877157519…13230780610602497279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.921 Γ— 10⁹⁢(97-digit number)
39219398959754315039…26461561221204994559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.843 Γ— 10⁹⁢(97-digit number)
78438797919508630079…52923122442409989119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.568 Γ— 10⁹⁷(98-digit number)
15687759583901726015…05846244884819978239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.137 Γ— 10⁹⁷(98-digit number)
31375519167803452031…11692489769639956479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.275 Γ— 10⁹⁷(98-digit number)
62751038335606904063…23384979539279912959
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:57,757,221 XPMΒ·at block #6,814,141 Β· updates every 60s
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