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Block #1,362,661

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/9/2015, 5:31:06 PM Β· Difficulty 10.8437 Β· 5,463,453 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d1770e1d8499e2caa7122fca8d4bdf2e5805497bb7f6f3b3fa746b244d8663c
View on Chainz β†—

Height

#1,362,661

Difficulty

10.843693

Transactions

2

Size

3.59 KB

Version

2

Bits

0ad7fc4b

Nonce

313,354,645

Timestamp

12/9/2015, 5:31:06 PM

Confirmations

5,463,453

Mined by

⛏️ P2SHATaNK2NmHgSjCFUbEjpKf159p2Uy8k6kAf

Merkle Root

0ef8d7a02b574612d1cd6311488058b1fcd150245d9e8ed38053073734bf0740
Transactions (2)
Coinbasecbc709746a78e3…8f56d1aea2383e
1 in β†’ 1 out8.5400 XPM110 B
ATaNK2Nm…Uy8k6kAf
6a362a35af6679…b34e576958edaf
23 in β†’ 2 out1032.0048 XPM3.39 KB
AZUb8bdL…7nyRTCQ2Ac7pezFw…DNBSHUwk
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.

5.013 Γ— 10⁹⁴(95-digit number)
50132933504886547582…87458658513186438399
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
5.013 Γ— 10⁹⁴(95-digit number)
50132933504886547582…87458658513186438399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁡(96-digit number)
10026586700977309516…74917317026372876799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.005 Γ— 10⁹⁡(96-digit number)
20053173401954619033…49834634052745753599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.010 Γ— 10⁹⁡(96-digit number)
40106346803909238066…99669268105491507199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.021 Γ— 10⁹⁡(96-digit number)
80212693607818476132…99338536210983014399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.604 Γ— 10⁹⁢(97-digit number)
16042538721563695226…98677072421966028799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.208 Γ— 10⁹⁢(97-digit number)
32085077443127390452…97354144843932057599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.417 Γ— 10⁹⁢(97-digit number)
64170154886254780905…94708289687864115199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.283 Γ— 10⁹⁷(98-digit number)
12834030977250956181…89416579375728230399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.566 Γ— 10⁹⁷(98-digit number)
25668061954501912362…78833158751456460799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.133 Γ— 10⁹⁷(98-digit number)
51336123909003824724…57666317502912921599
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:57,853,037 XPMΒ·at block #6,826,113 Β· updates every 60s
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