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Block #456,088

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/22/2014, 11:49:12 PM Β· Difficulty 10.4160 Β· 6,352,093 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f53a07bf7dba2686f24cbad47b1669d47be08839dc0491e174eacd0601fca6ca
View on Chainz β†—

Height

#456,088

Difficulty

10.416023

Transactions

1

Size

200 B

Version

2

Bits

0a6a807d

Nonce

42,799

Timestamp

3/22/2014, 11:49:12 PM

Confirmations

6,352,093

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ca5cdd53d357265082917b1109fb9ad3a6bea5aa99239ad5d1bc84376945d09e
Transactions (1)
Coinbaseca5cdd53d35726…bc84376945d09e
1 in β†’ 1 out9.2000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

8.690 Γ— 10⁹⁡(96-digit number)
86903761061452158547…00073910436842679259
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
8.690 Γ— 10⁹⁡(96-digit number)
86903761061452158547…00073910436842679259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.738 Γ— 10⁹⁢(97-digit number)
17380752212290431709…00147820873685358519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.476 Γ— 10⁹⁢(97-digit number)
34761504424580863419…00295641747370717039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.952 Γ— 10⁹⁢(97-digit number)
69523008849161726838…00591283494741434079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.390 Γ— 10⁹⁷(98-digit number)
13904601769832345367…01182566989482868159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.780 Γ— 10⁹⁷(98-digit number)
27809203539664690735…02365133978965736319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.561 Γ— 10⁹⁷(98-digit number)
55618407079329381470…04730267957931472639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.112 Γ— 10⁹⁸(99-digit number)
11123681415865876294…09460535915862945279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.224 Γ— 10⁹⁸(99-digit number)
22247362831731752588…18921071831725890559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.449 Γ— 10⁹⁸(99-digit number)
44494725663463505176…37842143663451781119
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:57,709,497 XPMΒ·at block #6,808,180 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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