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Block #144,117

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/1/2013, 2:53:59 AM Β· Difficulty 9.8380 Β· 6,654,912 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5fd7e48d7dcc8088da132d46373191b6abac7187908613bbf1488d0f2675b3a1
View on Chainz β†—

Height

#144,117

Difficulty

9.838011

Transactions

2

Size

391 B

Version

2

Bits

09d687de

Nonce

5,428

Timestamp

9/1/2013, 2:53:59 AM

Confirmations

6,654,912

Mined by

⛏️ P2SHAJnfGiH6Cj9xULG29yCUheZDdCRom3PedH

Merkle Root

49ce1e655f23b9454eaea0fdaf82a33348a9f342f650dd97dfe66ed90aec0a2a
Transactions (2)
Coinbase2bd65078bb508a…dfdae796c427ab
1 in β†’ 1 out10.3300 XPM109 B
AJnfGiH6…Rom3PedH
c582d19bd236d7…b882da1aedce80
1 in β†’ 1 out2.3151 XPM192 B
AKjsjTkW…7rGbLvxN
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.

7.470 Γ— 10⁹³(94-digit number)
74701838979362045733…44459848305159703039
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
7.470 Γ— 10⁹³(94-digit number)
74701838979362045733…44459848305159703039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.494 Γ— 10⁹⁴(95-digit number)
14940367795872409146…88919696610319406079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.988 Γ— 10⁹⁴(95-digit number)
29880735591744818293…77839393220638812159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.976 Γ— 10⁹⁴(95-digit number)
59761471183489636587…55678786441277624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.195 Γ— 10⁹⁡(96-digit number)
11952294236697927317…11357572882555248639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.390 Γ— 10⁹⁡(96-digit number)
23904588473395854634…22715145765110497279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.780 Γ— 10⁹⁡(96-digit number)
47809176946791709269…45430291530220994559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.561 Γ— 10⁹⁡(96-digit number)
95618353893583418539…90860583060441989119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.912 Γ— 10⁹⁢(97-digit number)
19123670778716683707…81721166120883978239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.824 Γ— 10⁹⁢(97-digit number)
38247341557433367415…63442332241767956479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,636,270 XPMΒ·at block #6,799,028 Β· updates every 60s
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