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Block #1,371,593

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2015, 2:35:59 PM Β· Difficulty 10.8109 Β· 5,471,404 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
faa5ab36b8fbd0f5b509fa8e0be0911fb1740ffef30b92dc366ab92694c2405d
View on Chainz β†—

Height

#1,371,593

Difficulty

10.810861

Transactions

1

Size

200 B

Version

2

Bits

0acf949d

Nonce

1,236,227,163

Timestamp

12/16/2015, 2:35:59 PM

Confirmations

5,471,404

Mined by

⛏️ P2SHAVkEPbhZ9BZLQPLmq3shPXNaY6sACADaWN

Merkle Root

1ae01267b5ca1cafabaa19e56acf174aea353a2bb5bb9fb168ded87fc06906ec
Transactions (1)
Coinbase1ae01267b5ca1c…ded87fc06906ec
1 in β†’ 1 out8.5400 XPM110 B
AVkEPbhZ…sACADaWN
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.

1.545 Γ— 10⁹⁡(96-digit number)
15456952452891567982…76615280676721238079
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
1.545 Γ— 10⁹⁡(96-digit number)
15456952452891567982…76615280676721238079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.091 Γ— 10⁹⁡(96-digit number)
30913904905783135965…53230561353442476159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.182 Γ— 10⁹⁡(96-digit number)
61827809811566271931…06461122706884952319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.236 Γ— 10⁹⁢(97-digit number)
12365561962313254386…12922245413769904639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.473 Γ— 10⁹⁢(97-digit number)
24731123924626508772…25844490827539809279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.946 Γ— 10⁹⁢(97-digit number)
49462247849253017545…51688981655079618559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.892 Γ— 10⁹⁢(97-digit number)
98924495698506035090…03377963310159237119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.978 Γ— 10⁹⁷(98-digit number)
19784899139701207018…06755926620318474239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.956 Γ— 10⁹⁷(98-digit number)
39569798279402414036…13511853240636948479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.913 Γ— 10⁹⁷(98-digit number)
79139596558804828072…27023706481273896959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.582 Γ— 10⁹⁸(99-digit number)
15827919311760965614…54047412962547793919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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
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