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Block #2,281,824

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2017, 8:29:47 AM Β· Difficulty 10.9555 Β· 4,562,216 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9a7cab1621e1e2dd4888128294b297e122b0625ad92b3f9fbe04572f952953f3
View on Chainz β†—

Height

#2,281,824

Difficulty

10.955496

Transactions

1

Size

200 B

Version

2

Bits

0af49b66

Nonce

61,011,132

Timestamp

9/4/2017, 8:29:47 AM

Confirmations

4,562,216

Mined by

⛏️ P2SHAeGdBFwzqy43d7fFin8SBBftcAJa6GhnuM

Merkle Root

d912f2e98e68dbf1f90fadf8a04588707ab44b72a9004f90c96fe61d2707b62e
Transactions (1)
Coinbased912f2e98e68db…6fe61d2707b62e
1 in β†’ 1 out8.3200 XPM110 B
AeGdBFwz…Ja6GhnuM
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.

1.595 Γ— 10⁹⁡(96-digit number)
15953082908616762836…23953833943577749441
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
1.595 Γ— 10⁹⁡(96-digit number)
15953082908616762836…23953833943577749441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.190 Γ— 10⁹⁡(96-digit number)
31906165817233525673…47907667887155498881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.381 Γ— 10⁹⁡(96-digit number)
63812331634467051346…95815335774310997761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.276 Γ— 10⁹⁢(97-digit number)
12762466326893410269…91630671548621995521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.552 Γ— 10⁹⁢(97-digit number)
25524932653786820538…83261343097243991041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.104 Γ— 10⁹⁢(97-digit number)
51049865307573641077…66522686194487982081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.020 Γ— 10⁹⁷(98-digit number)
10209973061514728215…33045372388975964161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.041 Γ— 10⁹⁷(98-digit number)
20419946123029456430…66090744777951928321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.083 Γ— 10⁹⁷(98-digit number)
40839892246058912861…32181489555903856641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.167 Γ— 10⁹⁷(98-digit number)
81679784492117825723…64362979111807713281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.633 Γ— 10⁹⁸(99-digit number)
16335956898423565144…28725958223615426561
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:57,996,689 XPMΒ·at block #6,844,039 Β· updates every 60s
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