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Block #216,768

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/18/2013, 10:19:57 PM Β· Difficulty 9.9274 Β· 6,579,793 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f3bcf584c647761ec2fcfd79dde95c17e91022edd6f103ac12e36793d2882237
View on Chainz β†—

Height

#216,768

Difficulty

9.927369

Transactions

1

Size

198 B

Version

2

Bits

09ed6813

Nonce

27,028

Timestamp

10/18/2013, 10:19:57 PM

Confirmations

6,579,793

Mined by

⛏️ P2SHAXHqpR716k7HAKyiRQyC63yPtEEXddpMfV

Merkle Root

e74a37b7bb510f31201cece6e0bb5cd889fb56a031f9870017100dee4fa83a18
Transactions (1)
Coinbasee74a37b7bb510f…100dee4fa83a18
1 in β†’ 1 out10.1300 XPM109 B
AXHqpR71…EXddpMfV
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.

1.738 Γ— 10⁹¹(92-digit number)
17382117133809602960…41129116306986741299
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
1.738 Γ— 10⁹¹(92-digit number)
17382117133809602960…41129116306986741299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.476 Γ— 10⁹¹(92-digit number)
34764234267619205921…82258232613973482599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.952 Γ— 10⁹¹(92-digit number)
69528468535238411842…64516465227946965199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.390 Γ— 10⁹²(93-digit number)
13905693707047682368…29032930455893930399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.781 Γ— 10⁹²(93-digit number)
27811387414095364737…58065860911787860799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.562 Γ— 10⁹²(93-digit number)
55622774828190729474…16131721823575721599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.112 Γ— 10⁹³(94-digit number)
11124554965638145894…32263443647151443199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.224 Γ— 10⁹³(94-digit number)
22249109931276291789…64526887294302886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.449 Γ— 10⁹³(94-digit number)
44498219862552583579…29053774588605772799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,616,487 XPMΒ·at block #6,796,560 Β· updates every 60s
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