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Block #2,169,037

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/20/2017, 4:26:01 PM Β· Difficulty 10.8986 Β· 4,673,177 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b7065291d702925cdce8c0f08f645aa16741639d293ef522ab169462daf592e1
View on Chainz β†—

Height

#2,169,037

Difficulty

10.898629

Transactions

2

Size

8.51 KB

Version

2

Bits

0ae60c8f

Nonce

1,887,675,113

Timestamp

6/20/2017, 4:26:01 PM

Confirmations

4,673,177

Mined by

⛏️ P2SHAH37T3Z6oTmGCgJr69oh8ivVLZuPTErXYk

Merkle Root

157fe073b593d6778f6e6c760662df0ab8411f0c4414f6b216ab58f5fc7abfd8
Transactions (2)
Coinbasea4dbc6bf8bf78f…d5f61dc8402f09
1 in β†’ 1 out8.5000 XPM109 B
AH37T3Z6…uPTErXYk
ad6a7100dd83bd…262da748071aff
57 in β†’ 2 out291.5809 XPM8.32 KB
AUoBdDi8…m7dZunoPAWYCa9BF…hVBpeLbf
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.

1.482 Γ— 10⁹⁴(95-digit number)
14828716518644197383…55400868783382509199
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
1.482 Γ— 10⁹⁴(95-digit number)
14828716518644197383…55400868783382509199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.482 Γ— 10⁹⁴(95-digit number)
14828716518644197383…55400868783382509201
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
2.965 Γ— 10⁹⁴(95-digit number)
29657433037288394767…10801737566765018399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.965 Γ— 10⁹⁴(95-digit number)
29657433037288394767…10801737566765018401
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
5.931 Γ— 10⁹⁴(95-digit number)
59314866074576789534…21603475133530036799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.931 Γ— 10⁹⁴(95-digit number)
59314866074576789534…21603475133530036801
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
1.186 Γ— 10⁹⁡(96-digit number)
11862973214915357906…43206950267060073599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.186 Γ— 10⁹⁡(96-digit number)
11862973214915357906…43206950267060073601
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
2.372 Γ— 10⁹⁡(96-digit number)
23725946429830715813…86413900534120147199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.372 Γ— 10⁹⁡(96-digit number)
23725946429830715813…86413900534120147201
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:57,982,109 XPMΒ·at block #6,842,213 Β· updates every 60s
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