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Block #196,540

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/6/2013, 1:32:35 PM Β· Difficulty 9.8810 Β· 6,599,211 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9d5b22ee27bf525ffe3d4ede854ee6998f55a90e44d920d22de2aa6a161909ca
View on Chainz β†—

Height

#196,540

Difficulty

9.881013

Transactions

1

Size

197 B

Version

2

Bits

09e18a0f

Nonce

60,560

Timestamp

10/6/2013, 1:32:35 PM

Confirmations

6,599,211

Mined by

⛏️ P2SHAKhaGKFX4s17sd56QzVFtsa8mSKjeAXtBv

Merkle Root

a5d0a01785f5b8c9915fa2054a9d3d742263947bda0d4c004e3922410c6b78df
Transactions (1)
Coinbasea5d0a01785f5b8…3922410c6b78df
1 in β†’ 1 out10.2300 XPM109 B
AKhaGKFX…KjeAXtBv
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.

3.549 Γ— 10⁸⁸(89-digit number)
35498480033303577225…04450488391063833059
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
3.549 Γ— 10⁸⁸(89-digit number)
35498480033303577225…04450488391063833059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.099 Γ— 10⁸⁸(89-digit number)
70996960066607154450…08900976782127666119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.419 Γ— 10⁸⁹(90-digit number)
14199392013321430890…17801953564255332239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.839 Γ— 10⁸⁹(90-digit number)
28398784026642861780…35603907128510664479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.679 Γ— 10⁸⁹(90-digit number)
56797568053285723560…71207814257021328959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.135 Γ— 10⁹⁰(91-digit number)
11359513610657144712…42415628514042657919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.271 Γ— 10⁹⁰(91-digit number)
22719027221314289424…84831257028085315839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.543 Γ— 10⁹⁰(91-digit number)
45438054442628578848…69662514056170631679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.087 Γ— 10⁹⁰(91-digit number)
90876108885257157697…39325028112341263359
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:57,610,087 XPMΒ·at block #6,795,750 Β· updates every 60s
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