XPM Prime Explorer symbol
XPMPrime Explorer

Block #583,508

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/10/2014, 4:01:24 PM Β· Difficulty 10.9569 Β· 6,219,770 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4f8d573f20439f0a91fb5ae84446c1ac18dfa45cae1d0e6470b9af49309a548d
View on Chainz β†—

Height

#583,508

Difficulty

10.956920

Transactions

1

Size

243 B

Version

2

Bits

0af4f8bd

Nonce

1,552,493,640

Timestamp

6/10/2014, 4:01:24 PM

Confirmations

6,219,770

Mined by

⛏️ P2SHAXn1KW6PTFKBcGVcbZ8CPoUc4Pc7VDu2zv

Merkle Root

ea5e65d734421fdd2d04ca6dc3a25bb63f9e0c20151e1e2594c76bad82ad3c90
Transactions (1)
Coinbaseea5e65d734421f…c76bad82ad3c90
1 in β†’ 2 out8.3200 XPM152 B
AXn1KW6P…c7VDu2zvALPu3s2c…EJXLjVFh
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.

2.295 Γ— 10⁹⁷(98-digit number)
22955680549203167234…46132739894529362461
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
2.295 Γ— 10⁹⁷(98-digit number)
22955680549203167234…46132739894529362461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.591 Γ— 10⁹⁷(98-digit number)
45911361098406334468…92265479789058724921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.182 Γ— 10⁹⁷(98-digit number)
91822722196812668937…84530959578117449841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.836 Γ— 10⁹⁸(99-digit number)
18364544439362533787…69061919156234899681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.672 Γ— 10⁹⁸(99-digit number)
36729088878725067574…38123838312469799361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.345 Γ— 10⁹⁸(99-digit number)
73458177757450135149…76247676624939598721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.469 Γ— 10⁹⁹(100-digit number)
14691635551490027029…52495353249879197441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.938 Γ— 10⁹⁹(100-digit number)
29383271102980054059…04990706499758394881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.876 Γ— 10⁹⁹(100-digit number)
58766542205960108119…09981412999516789761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.175 Γ— 10¹⁰⁰(101-digit number)
11753308441192021623…19962825999033579521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.350 Γ— 10¹⁰⁰(101-digit number)
23506616882384043247…39925651998067159041
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,670,250 XPMΒ·at block #6,803,277 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK