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Block #163,638

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 3:20:11 AM Β· Difficulty 9.8619 Β· 6,650,380 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
69782eee501b777898f847388d3733af86650b3a59cc5d2f776357ee3d295432
View on Chainz β†—

Height

#163,638

Difficulty

9.861923

Transactions

1

Size

199 B

Version

2

Bits

09dca6ff

Nonce

258,221

Timestamp

9/14/2013, 3:20:11 AM

Confirmations

6,650,380

Mined by

⛏️ P2SHAHNdTz9RdyhMpsaRttP7HwiXvgDHU2jpcA

Merkle Root

0a3d4509ecb45687bb47964cea5a12d2bd2600498caa39f1a57358d74a4038a1
Transactions (1)
Coinbase0a3d4509ecb456…7358d74a4038a1
1 in β†’ 1 out10.2700 XPM109 B
AHNdTz9R…DHU2jpcA
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.

1.689 Γ— 10⁹⁡(96-digit number)
16896207872734877151…74231704206265453439
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
1.689 Γ— 10⁹⁡(96-digit number)
16896207872734877151…74231704206265453439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.379 Γ— 10⁹⁡(96-digit number)
33792415745469754303…48463408412530906879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.758 Γ— 10⁹⁡(96-digit number)
67584831490939508606…96926816825061813759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.351 Γ— 10⁹⁢(97-digit number)
13516966298187901721…93853633650123627519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.703 Γ— 10⁹⁢(97-digit number)
27033932596375803442…87707267300247255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.406 Γ— 10⁹⁢(97-digit number)
54067865192751606884…75414534600494510079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.081 Γ— 10⁹⁷(98-digit number)
10813573038550321376…50829069200989020159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.162 Γ— 10⁹⁷(98-digit number)
21627146077100642753…01658138401978040319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.325 Γ— 10⁹⁷(98-digit number)
43254292154201285507…03316276803956080639
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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