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Block #86,102

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/27/2013, 9:40:58 PM Β· Difficulty 9.2904 Β· 6,721,053 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
157e0841bf9aa38e67a6eaf990a1185a55b2a29cb816f5fa535a83581a5ea75d
View on Chainz β†—

Height

#86,102

Difficulty

9.290399

Transactions

1

Size

200 B

Version

2

Bits

094a579d

Nonce

90,963

Timestamp

7/27/2013, 9:40:58 PM

Confirmations

6,721,053

Mined by

⛏️ P2SHASXW8s4r1QTq8Djg6zDrh4WCnULM8vqY9U

Merkle Root

edefc5647825311ed2a76d6dae7ad2dfef09dee3e91f389a0be002e93e4bee82
Transactions (1)
Coinbaseedefc564782531…e002e93e4bee82
1 in β†’ 1 out11.5700 XPM109 B
ASXW8s4r…LM8vqY9U
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.

1.218 Γ— 10⁹⁢(97-digit number)
12181748640828295354…05024672297428535961
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
1.218 Γ— 10⁹⁢(97-digit number)
12181748640828295354…05024672297428535961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.436 Γ— 10⁹⁢(97-digit number)
24363497281656590709…10049344594857071921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.872 Γ— 10⁹⁢(97-digit number)
48726994563313181418…20098689189714143841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.745 Γ— 10⁹⁢(97-digit number)
97453989126626362837…40197378379428287681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.949 Γ— 10⁹⁷(98-digit number)
19490797825325272567…80394756758856575361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.898 Γ— 10⁹⁷(98-digit number)
38981595650650545135…60789513517713150721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.796 Γ— 10⁹⁷(98-digit number)
77963191301301090270…21579027035426301441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.559 Γ— 10⁹⁸(99-digit number)
15592638260260218054…43158054070852602881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.118 Γ— 10⁹⁸(99-digit number)
31185276520520436108…86316108141705205761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,701,247 XPMΒ·at block #6,807,154 Β· updates every 60s
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