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Block #183,173

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/27/2013, 8:10:10 PM Β· Difficulty 9.8578 Β· 6,627,421 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2d88019839bd710079f2806f567a829028b0dfec82ef081b7660ec3e40876efc
View on Chainz β†—

Height

#183,173

Difficulty

9.857813

Transactions

1

Size

199 B

Version

2

Bits

09db99a6

Nonce

85,044

Timestamp

9/27/2013, 8:10:10 PM

Confirmations

6,627,421

Mined by

⛏️ P2SHAHPLSWVdVVmfZ1Mw8oxTBdXzN3ZdicvSUu

Merkle Root

a5a296018a6efa8ce0c4e5fbca14fd2d517b47a355d8703d7331de006986f243
Transactions (1)
Coinbasea5a296018a6efa…31de006986f243
1 in β†’ 1 out10.2800 XPM109 B
AHPLSWVd…ZdicvSUu
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.

4.229 Γ— 10⁹⁡(96-digit number)
42299135245137779506…90535355609583782879
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
4.229 Γ— 10⁹⁡(96-digit number)
42299135245137779506…90535355609583782879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.459 Γ— 10⁹⁡(96-digit number)
84598270490275559012…81070711219167565759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.691 Γ— 10⁹⁢(97-digit number)
16919654098055111802…62141422438335131519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.383 Γ— 10⁹⁢(97-digit number)
33839308196110223605…24282844876670263039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.767 Γ— 10⁹⁢(97-digit number)
67678616392220447210…48565689753340526079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.353 Γ— 10⁹⁷(98-digit number)
13535723278444089442…97131379506681052159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.707 Γ— 10⁹⁷(98-digit number)
27071446556888178884…94262759013362104319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.414 Γ— 10⁹⁷(98-digit number)
54142893113776357768…88525518026724208639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.082 Γ— 10⁹⁸(99-digit number)
10828578622755271553…77051036053448417279
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:57,728,839 XPMΒ·at block #6,810,593 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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