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Block #630,774

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2014, 4:33:38 AM Β· Difficulty 10.9616 Β· 6,194,357 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
757a822255123c6ffa6ed1d544fc0c1b40b40497de3c42799bcf6481a7679b90
View on Chainz β†—

Height

#630,774

Difficulty

10.961561

Transactions

2

Size

581 B

Version

2

Bits

0af628e1

Nonce

485,209,699

Timestamp

7/13/2014, 4:33:38 AM

Confirmations

6,194,357

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c51cceb571c46c12d4aab7414cfdbebdda8778ab48711eeba9a2ab876476bb3a
Transactions (2)
Coinbase1a14cfcabfc0cb…5a1b279aa354aa
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
87e40f3a8a6499…8aee69494fc933
2 in β†’ 2 out5.0880 XPM374 B
AMxnCb8G…TpGcToZkANia7wgK…VR264iFL
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.

4.185 Γ— 10⁹⁢(97-digit number)
41858687013045384361…87589277810807793839
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
4.185 Γ— 10⁹⁢(97-digit number)
41858687013045384361…87589277810807793839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.371 Γ— 10⁹⁢(97-digit number)
83717374026090768722…75178555621615587679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁷(98-digit number)
16743474805218153744…50357111243231175359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.348 Γ— 10⁹⁷(98-digit number)
33486949610436307488…00714222486462350719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.697 Γ— 10⁹⁷(98-digit number)
66973899220872614977…01428444972924701439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁸(99-digit number)
13394779844174522995…02856889945849402879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.678 Γ— 10⁹⁸(99-digit number)
26789559688349045991…05713779891698805759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.357 Γ— 10⁹⁸(99-digit number)
53579119376698091982…11427559783397611519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.071 Γ— 10⁹⁹(100-digit number)
10715823875339618396…22855119566795223039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.143 Γ— 10⁹⁹(100-digit number)
21431647750679236792…45710239133590446079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.286 Γ— 10⁹⁹(100-digit number)
42863295501358473585…91420478267180892159
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,845,132 XPMΒ·at block #6,825,130 Β· updates every 60s
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