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Block #157,070

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2013, 9:19:54 AM Β· Difficulty 9.8689 Β· 6,647,973 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b8154cd7afaf3bbcd8edc447fa15dacf79439b1250df386f8e4be687d8ab71db
View on Chainz β†—

Height

#157,070

Difficulty

9.868909

Transactions

1

Size

199 B

Version

2

Bits

09de70d6

Nonce

170,066

Timestamp

9/9/2013, 9:19:54 AM

Confirmations

6,647,973

Mined by

⛏️ P2SHAQE5juVGf2GjfXcDEExb1YTp8cv2LcRcDH

Merkle Root

662697aab4b5194ead376a5bedb097d49ffe2bf4c655ca3b9c2c0c1e17b3e630
Transactions (1)
Coinbase662697aab4b519…2c0c1e17b3e630
1 in β†’ 1 out10.2500 XPM109 B
AQE5juVG…v2LcRcDH
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.

1.784 Γ— 10⁹⁴(95-digit number)
17847692871589549147…06987573099293513279
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
1.784 Γ— 10⁹⁴(95-digit number)
17847692871589549147…06987573099293513279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.569 Γ— 10⁹⁴(95-digit number)
35695385743179098294…13975146198587026559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.139 Γ— 10⁹⁴(95-digit number)
71390771486358196589…27950292397174053119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.427 Γ— 10⁹⁡(96-digit number)
14278154297271639317…55900584794348106239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.855 Γ— 10⁹⁡(96-digit number)
28556308594543278635…11801169588696212479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.711 Γ— 10⁹⁡(96-digit number)
57112617189086557271…23602339177392424959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.142 Γ— 10⁹⁢(97-digit number)
11422523437817311454…47204678354784849919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.284 Γ— 10⁹⁢(97-digit number)
22845046875634622908…94409356709569699839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.569 Γ— 10⁹⁢(97-digit number)
45690093751269245817…88818713419139399679
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:57,684,409 XPMΒ·at block #6,805,042 Β· updates every 60s
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