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Block #774,988

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/19/2014, 3:31:35 AM Β· Difficulty 10.9820 Β· 6,033,812 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3c312cbbdaa9153256b5f4675fab63fc2822a4599711272b03747248dcd0f0d6
View on Chainz β†—

Height

#774,988

Difficulty

10.982026

Transactions

2

Size

431 B

Version

2

Bits

0afb6610

Nonce

2,644,615,452

Timestamp

10/19/2014, 3:31:35 AM

Confirmations

6,033,812

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f7d73a6c88aa04307e81054e8b1ce5901646661bbcf21ebf75fea154ad43b119
Transactions (2)
Coinbased80679311b71cb…24331c161e2e2e
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
0a3fe2e8dffc3b…7b9f82d342cb7f
1 in β†’ 2 out5.4904 XPM225 B
AMA1JjCx…bG9Y2mPMAUnf58LG…QFPFUdZ8
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.

1.155 Γ— 10⁹⁡(96-digit number)
11556389192040110048…76752225555968652959
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
1.155 Γ— 10⁹⁡(96-digit number)
11556389192040110048…76752225555968652959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.311 Γ— 10⁹⁡(96-digit number)
23112778384080220096…53504451111937305919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.622 Γ— 10⁹⁡(96-digit number)
46225556768160440192…07008902223874611839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.245 Γ— 10⁹⁡(96-digit number)
92451113536320880384…14017804447749223679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.849 Γ— 10⁹⁢(97-digit number)
18490222707264176076…28035608895498447359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.698 Γ— 10⁹⁢(97-digit number)
36980445414528352153…56071217790996894719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.396 Γ— 10⁹⁢(97-digit number)
73960890829056704307…12142435581993789439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.479 Γ— 10⁹⁷(98-digit number)
14792178165811340861…24284871163987578879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.958 Γ— 10⁹⁷(98-digit number)
29584356331622681722…48569742327975157759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.916 Γ— 10⁹⁷(98-digit number)
59168712663245363445…97139484655950315519
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:57,714,454 XPMΒ·at block #6,808,799 Β· updates every 60s
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