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Block #3,163,054

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2019, 7:16:35 AM Β· Difficulty 11.3055 Β· 3,678,940 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
90b911e1ac5bda119cdf3525d8a76cb4639c41bbd717af1658d8277b7f41ebd7
View on Chainz β†—

Height

#3,163,054

Difficulty

11.305472

Transactions

2

Size

14.35 KB

Version

2

Bits

0b4e3363

Nonce

499,508,130

Timestamp

5/1/2019, 7:16:35 AM

Confirmations

3,678,940

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

b2d8ef382c6d11a94e22d4bd78acb9da684c609e654c80781dba7619a9dcf036
Transactions (2)
Coinbase9efdb024877c35…d3d0e4b5cf6699
1 in β†’ 1 out7.9600 XPM110 B
AUMQRepm…tAfKmdW1
548dd351b4b0b1…1de82e609827ca
98 in β†’ 1 out393.2087 XPM14.15 KB
AWWtytp9…KRDQvtU2
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.

8.875 Γ— 10⁹⁴(95-digit number)
88750007568046722578…43957032776200050399
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
8.875 Γ— 10⁹⁴(95-digit number)
88750007568046722578…43957032776200050399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.775 Γ— 10⁹⁡(96-digit number)
17750001513609344515…87914065552400100799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.550 Γ— 10⁹⁡(96-digit number)
35500003027218689031…75828131104800201599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.100 Γ— 10⁹⁡(96-digit number)
71000006054437378062…51656262209600403199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.420 Γ— 10⁹⁢(97-digit number)
14200001210887475612…03312524419200806399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.840 Γ— 10⁹⁢(97-digit number)
28400002421774951225…06625048838401612799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.680 Γ— 10⁹⁢(97-digit number)
56800004843549902450…13250097676803225599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.136 Γ— 10⁹⁷(98-digit number)
11360000968709980490…26500195353606451199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.272 Γ— 10⁹⁷(98-digit number)
22720001937419960980…53000390707212902399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.544 Γ— 10⁹⁷(98-digit number)
45440003874839921960…06000781414425804799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.088 Γ— 10⁹⁷(98-digit number)
90880007749679843920…12001562828851609599
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:57,980,340 XPMΒ·at block #6,841,993 Β· updates every 60s
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