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Block #1,220,427

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/3/2015, 5:07:33 PM Β· Difficulty 10.7345 Β· 5,622,562 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
98bdc834491ed4cbcafe7bfac3366bde9c2ab86537cd3764bfc1e3fba20c1e8c
View on Chainz β†—

Height

#1,220,427

Difficulty

10.734469

Transactions

1

Size

200 B

Version

2

Bits

0abc062b

Nonce

451,669,513

Timestamp

9/3/2015, 5:07:33 PM

Confirmations

5,622,562

Mined by

⛏️ P2SHAbjt9ccUZjU8rN7dSvYQ2mkfSFY8WNkdou

Merkle Root

63fcd95747e202db4de559af213ad1aec1648951b88e40f1dea248eb84a9df15
Transactions (1)
Coinbase63fcd95747e202…a248eb84a9df15
1 in β†’ 1 out8.6600 XPM110 B
Abjt9ccU…Y8WNkdou
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.

3.299 Γ— 10⁹⁡(96-digit number)
32993881970268947426…69129994439002030079
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.299 Γ— 10⁹⁡(96-digit number)
32993881970268947426…69129994439002030079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.299 Γ— 10⁹⁡(96-digit number)
32993881970268947426…69129994439002030081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
6.598 Γ— 10⁹⁡(96-digit number)
65987763940537894853…38259988878004060159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.598 Γ— 10⁹⁡(96-digit number)
65987763940537894853…38259988878004060161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.319 Γ— 10⁹⁢(97-digit number)
13197552788107578970…76519977756008120319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.319 Γ— 10⁹⁢(97-digit number)
13197552788107578970…76519977756008120321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.639 Γ— 10⁹⁢(97-digit number)
26395105576215157941…53039955512016240639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.639 Γ— 10⁹⁢(97-digit number)
26395105576215157941…53039955512016240641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.279 Γ— 10⁹⁢(97-digit number)
52790211152430315883…06079911024032481279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.279 Γ— 10⁹⁢(97-digit number)
52790211152430315883…06079911024032481281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.055 Γ— 10⁹⁷(98-digit number)
10558042230486063176…12159822048064962559
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,988,268 XPMΒ·at block #6,842,988 Β· updates every 60s
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