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Block #2,830,209

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2018, 12:12:09 PM Β· Difficulty 11.7157 Β· 4,013,482 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
757d1ddf7fae60d7dd734140152c71fa823415128d83b7f4a9e3fd3d7ee87f4e
View on Chainz β†—

Height

#2,830,209

Difficulty

11.715693

Transactions

2

Size

425 B

Version

2

Bits

0bb737a8

Nonce

131,557,847

Timestamp

9/8/2018, 12:12:09 PM

Confirmations

4,013,482

Mined by

⛏️ P2SHAN9Yows1rMRcg91EyFCGgpuG2ybehPLqrA

Merkle Root

10404d40ea1d0812c34008e9e136fc6b3e9b55273101b78bccb07b61913c65bc
Transactions (2)
Coinbase12d6d6da4b019c…f125b6865f8aed
1 in β†’ 1 out7.2800 XPM110 B
AN9Yows1…behPLqrA
350e7c0a7ebd28…9cd2bb0e00bff0
1 in β†’ 2 out2.1929 XPM226 B
AQHdmkCb…Bf3EXSoUASQdb5nP…7oSVGsmb
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.

2.867 Γ— 10⁹³(94-digit number)
28670784556697583067…24393740035463252479
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
2.867 Γ— 10⁹³(94-digit number)
28670784556697583067…24393740035463252479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.867 Γ— 10⁹³(94-digit number)
28670784556697583067…24393740035463252481
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
5.734 Γ— 10⁹³(94-digit number)
57341569113395166135…48787480070926504959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.734 Γ— 10⁹³(94-digit number)
57341569113395166135…48787480070926504961
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
1.146 Γ— 10⁹⁴(95-digit number)
11468313822679033227…97574960141853009919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.146 Γ— 10⁹⁴(95-digit number)
11468313822679033227…97574960141853009921
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
2.293 Γ— 10⁹⁴(95-digit number)
22936627645358066454…95149920283706019839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.293 Γ— 10⁹⁴(95-digit number)
22936627645358066454…95149920283706019841
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
4.587 Γ— 10⁹⁴(95-digit number)
45873255290716132908…90299840567412039679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.587 Γ— 10⁹⁴(95-digit number)
45873255290716132908…90299840567412039681
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
9.174 Γ— 10⁹⁴(95-digit number)
91746510581432265816…80599681134824079359
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:57,993,899 XPMΒ·at block #6,843,690 Β· updates every 60s
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