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Block #43,876

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 10:08:30 PM Β· Difficulty 8.6872 Β· 6,773,439 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2a5d4ab4d7bc2f17a85fd382d1feb3f81962d1d89d21b1447dbe9fa06de9f67e
View on Chainz β†—

Height

#43,876

Difficulty

8.687159

Transactions

1

Size

203 B

Version

2

Bits

08afe9a4

Nonce

75

Timestamp

7/14/2013, 10:08:30 PM

Confirmations

6,773,439

Mined by

⛏️ P2SHAeqcQQm8QSjyKVH9cZSSztxFULjwV7zoVx

Merkle Root

07ad3270f71624f5dcc464b2afdb95ec2c8ba1461e11e53597a7b782d097fb3f
Transactions (1)
Coinbase07ad3270f71624…a7b782d097fb3f
1 in β†’ 1 out13.2300 XPM109 B
AeqcQQm8…jwV7zoVx
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.

5.710 Γ— 10¹⁰³(104-digit number)
57105891202238287082…87612794427363380799
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
5.710 Γ— 10¹⁰³(104-digit number)
57105891202238287082…87612794427363380799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.142 Γ— 10¹⁰⁴(105-digit number)
11421178240447657416…75225588854726761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.284 Γ— 10¹⁰⁴(105-digit number)
22842356480895314833…50451177709453523199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.568 Γ— 10¹⁰⁴(105-digit number)
45684712961790629666…00902355418907046399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.136 Γ— 10¹⁰⁴(105-digit number)
91369425923581259332…01804710837814092799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.827 Γ— 10¹⁰⁡(106-digit number)
18273885184716251866…03609421675628185599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.654 Γ— 10¹⁰⁡(106-digit number)
36547770369432503733…07218843351256371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.309 Γ— 10¹⁰⁡(106-digit number)
73095540738865007466…14437686702512742399
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:57,782,565 XPMΒ·at block #6,817,314 Β· updates every 60s
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