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Block #861,620

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/21/2014, 3:11:45 AM Β· Difficulty 10.9639 Β· 5,948,099 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9aa8f39b47f988766f01b0a0c2ad9b816629d1d351f90888bd87c2eeada9af32
View on Chainz β†—

Height

#861,620

Difficulty

10.963902

Transactions

2

Size

433 B

Version

2

Bits

0af6c24d

Nonce

2,237,091,357

Timestamp

12/21/2014, 3:11:45 AM

Confirmations

5,948,099

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f795446d1393f012a1d228436160821242d915ea588003beed1a647949aaa2a5
Transactions (2)
Coinbase0e1af7b8657816…d5f5d540fb66bc
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
2ccb3bbffab8a9…340620e7bf185f
1 in β†’ 2 out8862.3900 XPM226 B
AVYjh3Hg…jgGmvcVBASUDdu12…YS6UsfsU
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.

1.110 Γ— 10⁹⁷(98-digit number)
11100421006508811835…42759737460520504319
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
1.110 Γ— 10⁹⁷(98-digit number)
11100421006508811835…42759737460520504319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.220 Γ— 10⁹⁷(98-digit number)
22200842013017623671…85519474921041008639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.440 Γ— 10⁹⁷(98-digit number)
44401684026035247343…71038949842082017279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.880 Γ— 10⁹⁷(98-digit number)
88803368052070494686…42077899684164034559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.776 Γ— 10⁹⁸(99-digit number)
17760673610414098937…84155799368328069119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.552 Γ— 10⁹⁸(99-digit number)
35521347220828197874…68311598736656138239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.104 Γ— 10⁹⁸(99-digit number)
71042694441656395749…36623197473312276479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.420 Γ— 10⁹⁹(100-digit number)
14208538888331279149…73246394946624552959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.841 Γ— 10⁹⁹(100-digit number)
28417077776662558299…46492789893249105919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.683 Γ— 10⁹⁹(100-digit number)
56834155553325116599…92985579786498211839
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:57,721,832 XPMΒ·at block #6,809,718 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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