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Block #854,804

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/15/2014, 9:36:41 PM Β· Difficulty 10.9685 Β· 5,940,527 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3b5af7712671b97f4dd4132fae46c6116c0ffb47e1b6a59dc18f6dbbb4777126
View on Chainz β†—

Height

#854,804

Difficulty

10.968517

Transactions

2

Size

581 B

Version

2

Bits

0af7f0ba

Nonce

2,314,719,254

Timestamp

12/15/2014, 9:36:41 PM

Confirmations

5,940,527

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

383173271f962c96e7c7b4b0bc4c5ff7e868ccd9bfb918db3075c0c6c977c869
Transactions (2)
Coinbase265d892d2bf6ca…561269ed77d76a
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
cb2dc4fbfe2ade…8724aecef418c9
2 in β†’ 2 out25.9000 XPM373 B
AbfEn7Nt…55CdqUCRAZQBR9FY…6m28DxDG
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.

1.930 Γ— 10⁹⁸(99-digit number)
19306549319667875508…84600230037515550719
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
1.930 Γ— 10⁹⁸(99-digit number)
19306549319667875508…84600230037515550719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.861 Γ— 10⁹⁸(99-digit number)
38613098639335751016…69200460075031101439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.722 Γ— 10⁹⁸(99-digit number)
77226197278671502032…38400920150062202879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.544 Γ— 10⁹⁹(100-digit number)
15445239455734300406…76801840300124405759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.089 Γ— 10⁹⁹(100-digit number)
30890478911468600812…53603680600248811519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.178 Γ— 10⁹⁹(100-digit number)
61780957822937201625…07207361200497623039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.235 Γ— 10¹⁰⁰(101-digit number)
12356191564587440325…14414722400995246079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.471 Γ— 10¹⁰⁰(101-digit number)
24712383129174880650…28829444801990492159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.942 Γ— 10¹⁰⁰(101-digit number)
49424766258349761300…57658889603980984319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.884 Γ— 10¹⁰⁰(101-digit number)
98849532516699522601…15317779207961968639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.976 Γ— 10¹⁰¹(102-digit number)
19769906503339904520…30635558415923937279
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:57,606,706 XPMΒ·at block #6,795,330 Β· updates every 60s
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