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Block #1,617,233

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/7/2016, 2:16:53 AM Β· Difficulty 10.5814 Β· 5,209,975 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1429a13880b033ca9a045a62d21b292a682dfb08c398e37e622369fc975c4aea
View on Chainz β†—

Height

#1,617,233

Difficulty

10.581432

Transactions

2

Size

873 B

Version

2

Bits

0a94d8c1

Nonce

606,188,937

Timestamp

6/7/2016, 2:16:53 AM

Confirmations

5,209,975

Mined by

⛏️ P2SHALrhQ74ZZLJv3jQbJ89Eg3Nwcfj5kyUP5o

Merkle Root

5906a633e45f89ed194005c3dc51756ecb1013e3f550294e384ca86bb042acd8
Transactions (2)
Coinbasea84fb3b9d39fae…4e4ba37819d77c
1 in β†’ 1 out8.9300 XPM110 B
ALrhQ74Z…j5kyUP5o
d21f610b987b94…237c24db340b9b
4 in β†’ 2 out0.1574 XPM673 B
AaHpbS9D…1j4rpCrbAYj8y9fu…wtB3epbg
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.

1.437 Γ— 10⁹⁡(96-digit number)
14378223222918404876…91727707128640145921
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.437 Γ— 10⁹⁡(96-digit number)
14378223222918404876…91727707128640145921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.875 Γ— 10⁹⁡(96-digit number)
28756446445836809753…83455414257280291841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.751 Γ— 10⁹⁡(96-digit number)
57512892891673619506…66910828514560583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.150 Γ— 10⁹⁢(97-digit number)
11502578578334723901…33821657029121167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.300 Γ— 10⁹⁢(97-digit number)
23005157156669447802…67643314058242334721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.601 Γ— 10⁹⁢(97-digit number)
46010314313338895605…35286628116484669441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.202 Γ— 10⁹⁢(97-digit number)
92020628626677791210…70573256232969338881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.840 Γ— 10⁹⁷(98-digit number)
18404125725335558242…41146512465938677761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.680 Γ— 10⁹⁷(98-digit number)
36808251450671116484…82293024931877355521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.361 Γ— 10⁹⁷(98-digit number)
73616502901342232968…64586049863754711041
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,861,762 XPMΒ·at block #6,827,207 Β· updates every 60s
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