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Block #3,008,056

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2019, 4:02:47 PM Β· Difficulty 11.2037 Β· 3,834,970 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
443d03100bb87478966dc8298a0fc8653e09466a7e6e54cd83e59ff8c2590483
View on Chainz β†—

Height

#3,008,056

Difficulty

11.203728

Transactions

2

Size

1.86 KB

Version

2

Bits

0b34278d

Nonce

656,438,702

Timestamp

1/13/2019, 4:02:47 PM

Confirmations

3,834,970

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

76ee752a4ce7c43afcdfb35eed7df2981609e35ea6d56608c403097736ca2e68
Transactions (2)
Coinbase9228f31f4b61a3…e0d19d4b42b1cb
1 in β†’ 1 out7.9700 XPM110 B
AUMQRepm…tAfKmdW1
2bd68970f65228…00af5f5a5d0d87
11 in β†’ 2 out5830.0800 XPM1.66 KB
Abcq6hB7…nsWG27q2ANm65uxX…w5KG2EAJ
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.

6.683 Γ— 10⁹⁴(95-digit number)
66833591237453466146…95886689573693135839
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
6.683 Γ— 10⁹⁴(95-digit number)
66833591237453466146…95886689573693135839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.336 Γ— 10⁹⁡(96-digit number)
13366718247490693229…91773379147386271679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.673 Γ— 10⁹⁡(96-digit number)
26733436494981386458…83546758294772543359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.346 Γ— 10⁹⁡(96-digit number)
53466872989962772917…67093516589545086719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.069 Γ— 10⁹⁢(97-digit number)
10693374597992554583…34187033179090173439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.138 Γ— 10⁹⁢(97-digit number)
21386749195985109166…68374066358180346879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.277 Γ— 10⁹⁢(97-digit number)
42773498391970218333…36748132716360693759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.554 Γ— 10⁹⁢(97-digit number)
85546996783940436667…73496265432721387519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.710 Γ— 10⁹⁷(98-digit number)
17109399356788087333…46992530865442775039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.421 Γ— 10⁹⁷(98-digit number)
34218798713576174667…93985061730885550079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.843 Γ— 10⁹⁷(98-digit number)
68437597427152349334…87970123461771100159
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:57,988,562 XPMΒ·at block #6,843,025 Β· updates every 60s
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