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Block #906,892

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/23/2015, 5:22:21 PM Β· Difficulty 10.9354 Β· 5,899,024 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4feeb80792d08b3a55d93390a64edd7e2aef9c071da5d2e3b83feff9df290171
View on Chainz β†—

Height

#906,892

Difficulty

10.935368

Transactions

2

Size

4.32 KB

Version

2

Bits

0aef744b

Nonce

1,221,639,171

Timestamp

1/23/2015, 5:22:21 PM

Confirmations

5,899,024

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9810327d967889054e2064b619fa7f85f6c2d2ab4af686c8f370d0225d2b5f5b
Transactions (2)
Coinbase19abe468629267…4b41d181f492e1
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
9e05a7e4078725…f5c8b29d9c4602
28 in β†’ 2 out2969.4363 XPM4.12 KB
AKyJva1t…yt6mXxYJAcAFW717…V1pWEX3J
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.

7.314 Γ— 10⁹⁢(97-digit number)
73140121402890823477…79636213750439214079
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
7.314 Γ— 10⁹⁢(97-digit number)
73140121402890823477…79636213750439214079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.462 Γ— 10⁹⁷(98-digit number)
14628024280578164695…59272427500878428159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.925 Γ— 10⁹⁷(98-digit number)
29256048561156329391…18544855001756856319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.851 Γ— 10⁹⁷(98-digit number)
58512097122312658782…37089710003513712639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.170 Γ— 10⁹⁸(99-digit number)
11702419424462531756…74179420007027425279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.340 Γ— 10⁹⁸(99-digit number)
23404838848925063512…48358840014054850559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.680 Γ— 10⁹⁸(99-digit number)
46809677697850127025…96717680028109701119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.361 Γ— 10⁹⁸(99-digit number)
93619355395700254051…93435360056219402239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.872 Γ— 10⁹⁹(100-digit number)
18723871079140050810…86870720112438804479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.744 Γ— 10⁹⁹(100-digit number)
37447742158280101620…73741440224877608959
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:57,691,418 XPMΒ·at block #6,805,915 Β· updates every 60s
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