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Block #860,205

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/20/2014, 1:42:38 AM Β· Difficulty 10.9647 Β· 5,935,407 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee714e37ed5db7ae6a02eabf54777c24ee9dba471e1ef6d320780d0255cae14f
View on Chainz β†—

Height

#860,205

Difficulty

10.964673

Transactions

2

Size

874 B

Version

2

Bits

0af6f4c8

Nonce

1,150,554,029

Timestamp

12/20/2014, 1:42:38 AM

Confirmations

5,935,407

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b5cc6d17c4d90e952158d097d61465a06176cac055b633e8984ed4fda3752005
Transactions (2)
Coinbase4c7cb049115f09…df51042eea1e9c
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
5e43acc22b01ce…ae1b5fa00d2e7a
4 in β†’ 2 out2999.9100 XPM668 B
AQUC7Hue…LL2XMoNYAemShrK5…gpvHJKvd
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.

2.589 Γ— 10⁹⁡(96-digit number)
25892687766147248880…53374266272864509039
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
2.589 Γ— 10⁹⁡(96-digit number)
25892687766147248880…53374266272864509039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.178 Γ— 10⁹⁡(96-digit number)
51785375532294497761…06748532545729018079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.035 Γ— 10⁹⁢(97-digit number)
10357075106458899552…13497065091458036159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.071 Γ— 10⁹⁢(97-digit number)
20714150212917799104…26994130182916072319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.142 Γ— 10⁹⁢(97-digit number)
41428300425835598209…53988260365832144639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.285 Γ— 10⁹⁢(97-digit number)
82856600851671196418…07976520731664289279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.657 Γ— 10⁹⁷(98-digit number)
16571320170334239283…15953041463328578559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.314 Γ— 10⁹⁷(98-digit number)
33142640340668478567…31906082926657157119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.628 Γ— 10⁹⁷(98-digit number)
66285280681336957135…63812165853314314239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.325 Γ— 10⁹⁸(99-digit number)
13257056136267391427…27624331706628628479
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:57,608,961 XPMΒ·at block #6,795,611 Β· updates every 60s
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