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Block #1,476,155

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/28/2016, 10:06:36 PM Β· Difficulty 10.6978 Β· 5,368,865 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b4a35aa5b15bd5ce76dbffa31e56b59eee033ce2b79bdbe5455f851439a64386
View on Chainz β†—

Height

#1,476,155

Difficulty

10.697759

Transactions

1

Size

242 B

Version

2

Bits

0ab2a05b

Nonce

434,519,947

Timestamp

2/28/2016, 10:06:36 PM

Confirmations

5,368,865

Mined by

⛏️ P2SHAG5qp4HQNAk5AGjAsgiB4hsSTAxTE9E9fF

Merkle Root

a604f84d8224256b83c38e614784e26fcb17db5fe2f715975b488bad66ff108f
Transactions (1)
Coinbasea604f84d822425…488bad66ff108f
1 in β†’ 2 out8.7200 XPM152 B
AG5qp4HQ…xTE9E9fFALPu3s2c…EJXLjVFh
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.

4.402 Γ— 10⁹⁴(95-digit number)
44027363735969553290…52775137054315480319
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
4.402 Γ— 10⁹⁴(95-digit number)
44027363735969553290…52775137054315480319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.805 Γ— 10⁹⁴(95-digit number)
88054727471939106581…05550274108630960639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.761 Γ— 10⁹⁡(96-digit number)
17610945494387821316…11100548217261921279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.522 Γ— 10⁹⁡(96-digit number)
35221890988775642632…22201096434523842559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.044 Γ— 10⁹⁡(96-digit number)
70443781977551285264…44402192869047685119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.408 Γ— 10⁹⁢(97-digit number)
14088756395510257052…88804385738095370239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.817 Γ— 10⁹⁢(97-digit number)
28177512791020514105…77608771476190740479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.635 Γ— 10⁹⁢(97-digit number)
56355025582041028211…55217542952381480959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.127 Γ— 10⁹⁷(98-digit number)
11271005116408205642…10435085904762961919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.254 Γ— 10⁹⁷(98-digit number)
22542010232816411284…20870171809525923839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.508 Γ— 10⁹⁷(98-digit number)
45084020465632822569…41740343619051847679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,004,584 XPMΒ·at block #6,845,019 Β· updates every 60s
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