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Block #2,783,318

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2018, 12:32:36 PM Β· Difficulty 11.6630 Β· 4,057,542 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
980133ee17f82a5488f07dc155c43d8f50f0d955e900446b2b91851a2665627e
View on Chainz β†—

Height

#2,783,318

Difficulty

11.662981

Transactions

2

Size

689 B

Version

2

Bits

0ba9b923

Nonce

490,209,466

Timestamp

8/7/2018, 12:32:36 PM

Confirmations

4,057,542

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

490d2667d401bd3e8a85defa406be2ee6706937b73e5752b1b4f6f14553b1f0a
Transactions (2)
Coinbase364a68f0243ebd…aec3a8d497dded
1 in β†’ 1 out7.3500 XPM110 B
AZtxQr2F…7grUWrUz
ec91a6dd266d47…599433e0b8a587
3 in β†’ 2 out10.1667 XPM488 B
AVmouKc6…8KbU6rEMAXZMRcXr…z2dUbCSR
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.

4.175 Γ— 10⁹⁷(98-digit number)
41755446064396799597…44465012841096821759
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
4.175 Γ— 10⁹⁷(98-digit number)
41755446064396799597…44465012841096821759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.351 Γ— 10⁹⁷(98-digit number)
83510892128793599194…88930025682193643519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.670 Γ— 10⁹⁸(99-digit number)
16702178425758719838…77860051364387287039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.340 Γ— 10⁹⁸(99-digit number)
33404356851517439677…55720102728774574079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.680 Γ— 10⁹⁸(99-digit number)
66808713703034879355…11440205457549148159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.336 Γ— 10⁹⁹(100-digit number)
13361742740606975871…22880410915098296319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.672 Γ— 10⁹⁹(100-digit number)
26723485481213951742…45760821830196592639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.344 Γ— 10⁹⁹(100-digit number)
53446970962427903484…91521643660393185279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.068 Γ— 10¹⁰⁰(101-digit number)
10689394192485580696…83043287320786370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.137 Γ— 10¹⁰⁰(101-digit number)
21378788384971161393…66086574641572741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.275 Γ— 10¹⁰⁰(101-digit number)
42757576769942322787…32173149283145482239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
8.551 Γ— 10¹⁰⁰(101-digit number)
85515153539884645575…64346298566290964479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,971,227 XPMΒ·at block #6,840,859 Β· updates every 60s
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