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Block #2,051,487

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2017, 1:08:52 PM Β· Difficulty 10.7154 Β· 4,790,528 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a5b6b9666a57033d174fc7c6f4eab40819efadd657962db678d274154bbac201
View on Chainz β†—

Height

#2,051,487

Difficulty

10.715382

Transactions

1

Size

200 B

Version

2

Bits

0ab72343

Nonce

22,407,969

Timestamp

4/3/2017, 1:08:52 PM

Confirmations

4,790,528

Mined by

⛏️ P2SHAQS6oJCQu9Jx3gtmWy4WqkHo9Xa9uWqLBq

Merkle Root

3a4091883864ff41ad1fe28a6f430bd274f9f6c8db7a5d4f4a2cf89dead1b7cb
Transactions (1)
Coinbase3a4091883864ff…2cf89dead1b7cb
1 in β†’ 1 out8.7000 XPM110 B
AQS6oJCQ…a9uWqLBq
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.

7.520 Γ— 10⁹⁡(96-digit number)
75205673770231970545…55929620770938562559
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
7.520 Γ— 10⁹⁡(96-digit number)
75205673770231970545…55929620770938562559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.520 Γ— 10⁹⁡(96-digit number)
75205673770231970545…55929620770938562561
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
1.504 Γ— 10⁹⁢(97-digit number)
15041134754046394109…11859241541877125119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.504 Γ— 10⁹⁢(97-digit number)
15041134754046394109…11859241541877125121
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
3.008 Γ— 10⁹⁢(97-digit number)
30082269508092788218…23718483083754250239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.008 Γ— 10⁹⁢(97-digit number)
30082269508092788218…23718483083754250241
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
6.016 Γ— 10⁹⁢(97-digit number)
60164539016185576436…47436966167508500479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.016 Γ— 10⁹⁢(97-digit number)
60164539016185576436…47436966167508500481
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
1.203 Γ— 10⁹⁷(98-digit number)
12032907803237115287…94873932335017000959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.203 Γ— 10⁹⁷(98-digit number)
12032907803237115287…94873932335017000961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
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 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:57,980,506 XPMΒ·at block #6,842,014 Β· updates every 60s
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