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Block #173,462

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/21/2013, 12:24:01 AM Β· Difficulty 9.8603 Β· 6,623,396 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fd7fb9954e33118e6c81d8ab1667349913f915e4ff8951c48c8ca0961d0e80a7
View on Chainz β†—

Height

#173,462

Difficulty

9.860333

Transactions

2

Size

361 B

Version

2

Bits

09dc3ecc

Nonce

54,224

Timestamp

9/21/2013, 12:24:01 AM

Confirmations

6,623,396

Mined by

⛏️ P2SHAWbQMT1UFX9Fb1nejhFo5DMbcK8Pt4ow7J

Merkle Root

30acf1f1a93cd7af0e3016fc50f6f2b692b03cabbdad9f8f654e97b955bda9b2
Transactions (2)
Coinbasea5277fb229bf85…9f323a6bb91f93
1 in β†’ 1 out10.2800 XPM109 B
AWbQMT1U…8Pt4ow7J
bdf37a9bc8cf49…0d124d7066d9bf
1 in β†’ 1 out10.3100 XPM159 B
AY5L1chV…SqfWvt6Z
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.

1.662 Γ— 10¹⁰²(103-digit number)
16626786644779956778…98453373226785177599
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
1.662 Γ— 10¹⁰²(103-digit number)
16626786644779956778…98453373226785177599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.325 Γ— 10¹⁰²(103-digit number)
33253573289559913557…96906746453570355199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.650 Γ— 10¹⁰²(103-digit number)
66507146579119827115…93813492907140710399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.330 Γ— 10¹⁰³(104-digit number)
13301429315823965423…87626985814281420799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.660 Γ— 10¹⁰³(104-digit number)
26602858631647930846…75253971628562841599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.320 Γ— 10¹⁰³(104-digit number)
53205717263295861692…50507943257125683199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.064 Γ— 10¹⁰⁴(105-digit number)
10641143452659172338…01015886514251366399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.128 Γ— 10¹⁰⁴(105-digit number)
21282286905318344676…02031773028502732799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.256 Γ— 10¹⁰⁴(105-digit number)
42564573810636689353…04063546057005465599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.512 Γ— 10¹⁰⁴(105-digit number)
85129147621273378707…08127092114010931199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,618,877 XPMΒ·at block #6,796,857 Β· updates every 60s
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