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Block #74,278

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 10:15:13 AM Β· Difficulty 8.9954 Β· 6,729,420 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c7e41473e89fb781017babe06b2d812ac7a5bada3855f4ef2c615e5757351d9d
View on Chainz β†—

Height

#74,278

Difficulty

8.995405

Transactions

2

Size

422 B

Version

2

Bits

08fed2de

Nonce

98

Timestamp

7/21/2013, 10:15:13 AM

Confirmations

6,729,420

Mined by

⛏️ P2SHAKbWY8af7GeucAvsHH136KjTirW7fFsmVJ

Merkle Root

b4ab3d7e1b04d04ef8d48820e1833b8ad9f7ab72f6a71f0fe1047d9feb64f667
Transactions (2)
Coinbase0ae305ad04e405…64ab6e9eabeef7
1 in β†’ 1 out12.3500 XPM110 B
AKbWY8af…W7fFsmVJ
979bbe3d5390dd…19871f5379fa90
1 in β†’ 2 out11.9900 XPM226 B
ARP8QpQi…sFuEcay7AUFV2zjt…R3g2b5n6
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.

1.389 Γ— 10⁸⁢(87-digit number)
13893724603849480476…77784443472278630079
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
1.389 Γ— 10⁸⁢(87-digit number)
13893724603849480476…77784443472278630079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.778 Γ— 10⁸⁢(87-digit number)
27787449207698960953…55568886944557260159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.557 Γ— 10⁸⁢(87-digit number)
55574898415397921907…11137773889114520319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.111 Γ— 10⁸⁷(88-digit number)
11114979683079584381…22275547778229040639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.222 Γ— 10⁸⁷(88-digit number)
22229959366159168762…44551095556458081279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.445 Γ— 10⁸⁷(88-digit number)
44459918732318337525…89102191112916162559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.891 Γ— 10⁸⁷(88-digit number)
88919837464636675051…78204382225832325119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.778 Γ— 10⁸⁸(89-digit number)
17783967492927335010…56408764451664650239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.556 Γ— 10⁸⁸(89-digit number)
35567934985854670020…12817528903329300479
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,673,622 XPMΒ·at block #6,803,697 Β· updates every 60s
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