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Block #71,476

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 6:53:07 PM Β· Difficulty 8.9932 Β· 6,735,146 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a2968c985aa1834e0df807168346e10bc167f884213e162608652f33073e1e69
View on Chainz β†—

Height

#71,476

Difficulty

8.993226

Transactions

1

Size

201 B

Version

2

Bits

08fe4411

Nonce

265

Timestamp

7/20/2013, 6:53:07 PM

Confirmations

6,735,146

Mined by

⛏️ P2SHANYe8KyPCpPzPnuRkCeGwL6TTHt58nkW75

Merkle Root

7c472e06028e75f2d156da45d3d47bc718dd673eebc22d3ad548c946b2ad1dc2
Transactions (1)
Coinbase7c472e06028e75…48c946b2ad1dc2
1 in β†’ 1 out12.3500 XPM110 B
ANYe8KyP…t58nkW75
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.

1.695 Γ— 10⁹⁢(97-digit number)
16953099132783417805…68888842663273569439
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
1.695 Γ— 10⁹⁢(97-digit number)
16953099132783417805…68888842663273569439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.390 Γ— 10⁹⁢(97-digit number)
33906198265566835611…37777685326547138879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.781 Γ— 10⁹⁢(97-digit number)
67812396531133671222…75555370653094277759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.356 Γ— 10⁹⁷(98-digit number)
13562479306226734244…51110741306188555519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.712 Γ— 10⁹⁷(98-digit number)
27124958612453468488…02221482612377111039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.424 Γ— 10⁹⁷(98-digit number)
54249917224906936977…04442965224754222079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.084 Γ— 10⁹⁸(99-digit number)
10849983444981387395…08885930449508444159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.169 Γ— 10⁹⁸(99-digit number)
21699966889962774791…17771860899016888319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,697,077 XPMΒ·at block #6,806,621 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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