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Block #103,607

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2013, 4:24:29 PM Β· Difficulty 9.5306 Β· 6,714,366 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
44cdd046cea71a718f91f4fdedad5812ca04e747a3589c5c3db499d7ba6a4adf
View on Chainz β†—

Height

#103,607

Difficulty

9.530640

Transactions

1

Size

200 B

Version

2

Bits

0987d801

Nonce

895

Timestamp

8/7/2013, 4:24:29 PM

Confirmations

6,714,366

Mined by

⛏️ P2SHAM4yfzq9kd5ymxEmqWi4GMBjWNLcimorTV

Merkle Root

2d7922bd736b8e72cb2b31ec41810e8ce83f30caceff33054dc30aa1624bf618
Transactions (1)
Coinbase2d7922bd736b8e…c30aa1624bf618
1 in β†’ 1 out10.9900 XPM109 B
AM4yfzq9…LcimorTV
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.

1.348 Γ— 10⁹⁸(99-digit number)
13484250446299813284…54041613497742336379
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
1.348 Γ— 10⁹⁸(99-digit number)
13484250446299813284…54041613497742336379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.696 Γ— 10⁹⁸(99-digit number)
26968500892599626569…08083226995484672759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.393 Γ— 10⁹⁸(99-digit number)
53937001785199253139…16166453990969345519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.078 Γ— 10⁹⁹(100-digit number)
10787400357039850627…32332907981938691039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.157 Γ— 10⁹⁹(100-digit number)
21574800714079701255…64665815963877382079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.314 Γ— 10⁹⁹(100-digit number)
43149601428159402511…29331631927754764159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.629 Γ— 10⁹⁹(100-digit number)
86299202856318805022…58663263855509528319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.725 Γ— 10¹⁰⁰(101-digit number)
17259840571263761004…17326527711019056639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.451 Γ— 10¹⁰⁰(101-digit number)
34519681142527522008…34653055422038113279
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:57,787,855 XPMΒ·at block #6,817,972 Β· updates every 60s
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