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Block #1,147,483

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/9/2015, 8:46:38 PM Β· Difficulty 10.9382 Β· 5,657,328 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9798724ad71024391fde94db103917dfce4ea2711e3ec4db00c7e7a8dc6e907e
View on Chainz β†—

Height

#1,147,483

Difficulty

10.938235

Transactions

2

Size

424 B

Version

2

Bits

0af03023

Nonce

375,268,400

Timestamp

7/9/2015, 8:46:38 PM

Confirmations

5,657,328

Mined by

⛏️ P2SHAKNwVYszfqBAuLUHZHJ2iXjzs8dmS27SHU

Merkle Root

3ca564614b747726b723be43a007a7155db9bcd10dd8aec211da52f7d5ab5d30
Transactions (2)
Coinbase2abec430ce73f4…846776a8950aaf
1 in β†’ 1 out8.3500 XPM109 B
AKNwVYsz…dmS27SHU
c30cf3d74fa89d…2bd2c0dbd3a002
1 in β†’ 2 out1.1760 XPM226 B
AGt5WAA6…SNrUjFk6AX4WQ8Gn…4nCZtmpL
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.

5.514 Γ— 10⁹²(93-digit number)
55145413302632792338…80670213902612880639
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
5.514 Γ— 10⁹²(93-digit number)
55145413302632792338…80670213902612880639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.102 Γ— 10⁹³(94-digit number)
11029082660526558467…61340427805225761279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.205 Γ— 10⁹³(94-digit number)
22058165321053116935…22680855610451522559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.411 Γ— 10⁹³(94-digit number)
44116330642106233871…45361711220903045119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.823 Γ— 10⁹³(94-digit number)
88232661284212467742…90723422441806090239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.764 Γ— 10⁹⁴(95-digit number)
17646532256842493548…81446844883612180479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.529 Γ— 10⁹⁴(95-digit number)
35293064513684987096…62893689767224360959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.058 Γ— 10⁹⁴(95-digit number)
70586129027369974193…25787379534448721919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.411 Γ— 10⁹⁡(96-digit number)
14117225805473994838…51574759068897443839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.823 Γ— 10⁹⁡(96-digit number)
28234451610947989677…03149518137794887679
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:57,682,556 XPMΒ·at block #6,804,810 Β· updates every 60s
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