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Block #1,610,558

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/2/2016, 5:23:43 AM Β· Difficulty 10.6080 Β· 5,234,076 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6984a765bbf1c54f16a35883bdfcf538f5a1bbedc7e524aabebf1b804fb8659a
View on Chainz β†—

Height

#1,610,558

Difficulty

10.608030

Transactions

1

Size

199 B

Version

2

Bits

0a9ba7da

Nonce

2,049,737,474

Timestamp

6/2/2016, 5:23:43 AM

Confirmations

5,234,076

Mined by

⛏️ P2SHAJW3ksWHaRjSM5gbVHbAtCVhk4xeKwYuxX

Merkle Root

76074daac22f428dbf6d25f4fa16660db083e63236e355b879871f2ebcd2f00c
Transactions (1)
Coinbase76074daac22f42…871f2ebcd2f00c
1 in β†’ 1 out8.8700 XPM109 B
AJW3ksWH…xeKwYuxX
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.

1.947 Γ— 10⁹⁡(96-digit number)
19479717523187510218…17401708953866617279
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
1.947 Γ— 10⁹⁡(96-digit number)
19479717523187510218…17401708953866617279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.895 Γ— 10⁹⁡(96-digit number)
38959435046375020436…34803417907733234559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.791 Γ— 10⁹⁡(96-digit number)
77918870092750040872…69606835815466469119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.558 Γ— 10⁹⁢(97-digit number)
15583774018550008174…39213671630932938239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.116 Γ— 10⁹⁢(97-digit number)
31167548037100016349…78427343261865876479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.233 Γ— 10⁹⁢(97-digit number)
62335096074200032698…56854686523731752959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.246 Γ— 10⁹⁷(98-digit number)
12467019214840006539…13709373047463505919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.493 Γ— 10⁹⁷(98-digit number)
24934038429680013079…27418746094927011839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.986 Γ— 10⁹⁷(98-digit number)
49868076859360026158…54837492189854023679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.973 Γ— 10⁹⁷(98-digit number)
99736153718720052317…09674984379708047359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:58,001,478 XPMΒ·at block #6,844,633 Β· updates every 60s
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