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Block #61,949

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 4:13:34 PM Β· Difficulty 8.9749 Β· 6,748,905 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7c86f915a511de5d63de312a5bd362e8c7ed0be8d4533425666688a8f3307db5
View on Chainz β†—

Height

#61,949

Difficulty

8.974875

Transactions

1

Size

200 B

Version

2

Bits

08f99165

Nonce

630

Timestamp

7/18/2013, 4:13:34 PM

Confirmations

6,748,905

Mined by

⛏️ P2SHAee3VTFJGSvZkYd1eE8HApV5mA4a27jmyV

Merkle Root

266471a8bbbc6e5d291a3c2efe228dcc355b765cb3a56dbc1a3a4a7fc85b867f
Transactions (1)
Coinbase266471a8bbbc6e…3a4a7fc85b867f
1 in β†’ 1 out12.4000 XPM109 B
Aee3VTFJ…4a27jmyV
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.

3.356 Γ— 10⁹⁢(97-digit number)
33568872593982673499…89653635268235123599
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
3.356 Γ— 10⁹⁢(97-digit number)
33568872593982673499…89653635268235123599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.713 Γ— 10⁹⁢(97-digit number)
67137745187965346999…79307270536470247199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.342 Γ— 10⁹⁷(98-digit number)
13427549037593069399…58614541072940494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.685 Γ— 10⁹⁷(98-digit number)
26855098075186138799…17229082145880988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.371 Γ— 10⁹⁷(98-digit number)
53710196150372277599…34458164291761977599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁸(99-digit number)
10742039230074455519…68916328583523955199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.148 Γ— 10⁹⁸(99-digit number)
21484078460148911039…37832657167047910399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.296 Γ— 10⁹⁸(99-digit number)
42968156920297822079…75665314334095820799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.593 Γ— 10⁹⁸(99-digit number)
85936313840595644159…51330628668191641599
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:57,730,929 XPMΒ·at block #6,810,853 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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