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Block #179,202

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/24/2013, 10:14:59 PM Β· Difficulty 9.8636 Β· 6,628,248 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
518bed53bf67e6373226b5a3eb37b75ca2f8ab0272a193c0403f841f151a6688
View on Chainz β†—

Height

#179,202

Difficulty

9.863617

Transactions

2

Size

425 B

Version

2

Bits

09dd1602

Nonce

21,986

Timestamp

9/24/2013, 10:14:59 PM

Confirmations

6,628,248

Mined by

⛏️ P2SHAf1jBCF7UBADhkLiwaffgAYsLv35c6Urby

Merkle Root

349cca4282142a33fa2af60b75690d56d2281eff33f4d89170123aa634afa64d
Transactions (2)
Coinbase6c352054098984…45f3a0ff698ec8
1 in β†’ 1 out10.2700 XPM109 B
Af1jBCF7…35c6Urby
4eb33f12037118…89e9ea9843f29d
1 in β†’ 2 out5.1525 XPM226 B
AFqPVcR9…cZf8zFFDATuWxsBa…dKFZ3gRq
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.

2.789 Γ— 10⁹⁴(95-digit number)
27895775939379831562…38280149616027963359
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
2.789 Γ— 10⁹⁴(95-digit number)
27895775939379831562…38280149616027963359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.579 Γ— 10⁹⁴(95-digit number)
55791551878759663124…76560299232055926719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.115 Γ— 10⁹⁡(96-digit number)
11158310375751932624…53120598464111853439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.231 Γ— 10⁹⁡(96-digit number)
22316620751503865249…06241196928223706879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.463 Γ— 10⁹⁡(96-digit number)
44633241503007730499…12482393856447413759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.926 Γ— 10⁹⁡(96-digit number)
89266483006015460999…24964787712894827519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.785 Γ— 10⁹⁢(97-digit number)
17853296601203092199…49929575425789655039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.570 Γ— 10⁹⁢(97-digit number)
35706593202406184399…99859150851579310079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.141 Γ— 10⁹⁢(97-digit number)
71413186404812368799…99718301703158620159
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:57,703,623 XPMΒ·at block #6,807,449 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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