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Block #156,672

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2013, 2:57:34 AM Β· Difficulty 9.8685 Β· 6,653,241 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51d95b8fc74cc388b71594af652a2bf8f7d664a47336a110a07b99ac6568f1cb
View on Chainz β†—

Height

#156,672

Difficulty

9.868507

Transactions

1

Size

201 B

Version

2

Bits

09de5672

Nonce

245,519

Timestamp

9/9/2013, 2:57:34 AM

Confirmations

6,653,241

Mined by

⛏️ P2SHAJQ7bqzh8jMKwbhminzZ7vurTxoY2ANRaW

Merkle Root

bd2cc4f19decd1d296d7ceeb00fb2b8719ecb0702ddd51d3618141ec28e6644a
Transactions (1)
Coinbasebd2cc4f19decd1…8141ec28e6644a
1 in β†’ 1 out10.2500 XPM110 B
AJQ7bqzh…oY2ANRaW
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.

6.087 Γ— 10⁹⁢(97-digit number)
60877877275943033193…66245673722452426879
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
6.087 Γ— 10⁹⁢(97-digit number)
60877877275943033193…66245673722452426879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.217 Γ— 10⁹⁷(98-digit number)
12175575455188606638…32491347444904853759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.435 Γ— 10⁹⁷(98-digit number)
24351150910377213277…64982694889809707519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.870 Γ— 10⁹⁷(98-digit number)
48702301820754426554…29965389779619415039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.740 Γ— 10⁹⁷(98-digit number)
97404603641508853109…59930779559238830079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.948 Γ— 10⁹⁸(99-digit number)
19480920728301770621…19861559118477660159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.896 Γ— 10⁹⁸(99-digit number)
38961841456603541243…39723118236955320319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.792 Γ— 10⁹⁸(99-digit number)
77923682913207082487…79446236473910640639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.558 Γ— 10⁹⁹(100-digit number)
15584736582641416497…58892472947821281279
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:57,723,388 XPMΒ·at block #6,809,912 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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