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Block #209,987

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2013, 9:16:55 PM Β· Difficulty 9.9118 Β· 6,615,351 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
989b170c622507446e396a98e90298b53e658f5f1d9b3209362b2e76fb0d1f4d
View on Chainz β†—

Height

#209,987

Difficulty

9.911756

Transactions

1

Size

196 B

Version

2

Bits

09e968d0

Nonce

246,627

Timestamp

10/14/2013, 9:16:55 PM

Confirmations

6,615,351

Mined by

⛏️ P2SHAK7kWkL4sngiZYayFhX74gnWY2GHfWFBHC

Merkle Root

47896df7e3cdce95cd324ca53e803ac5b8ee7d9749cda5d79b8a065ed4c92912
Transactions (1)
Coinbase47896df7e3cdce…8a065ed4c92912
1 in β†’ 1 out10.1600 XPM109 B
AK7kWkL4…GHfWFBHC
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.

2.249 Γ— 10⁸⁸(89-digit number)
22493702270171759840…00159787914797495439
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
2.249 Γ— 10⁸⁸(89-digit number)
22493702270171759840…00159787914797495439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.498 Γ— 10⁸⁸(89-digit number)
44987404540343519681…00319575829594990879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.997 Γ— 10⁸⁸(89-digit number)
89974809080687039362…00639151659189981759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.799 Γ— 10⁸⁹(90-digit number)
17994961816137407872…01278303318379963519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.598 Γ— 10⁸⁹(90-digit number)
35989923632274815745…02556606636759927039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.197 Γ— 10⁸⁹(90-digit number)
71979847264549631490…05113213273519854079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.439 Γ— 10⁹⁰(91-digit number)
14395969452909926298…10226426547039708159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.879 Γ— 10⁹⁰(91-digit number)
28791938905819852596…20452853094079416319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.758 Γ— 10⁹⁰(91-digit number)
57583877811639705192…40905706188158832639
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
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