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Block #2,660,055

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/14/2018, 2:59:07 AM Β· Difficulty 11.6386 Β· 4,184,062 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e72a63a3694c6baeaa1363b4c0501d2d6c2a8e31df38e10d7d2804b0de69f0be
View on Chainz β†—

Height

#2,660,055

Difficulty

11.638568

Transactions

2

Size

1.14 KB

Version

2

Bits

0ba3792b

Nonce

711,904,192

Timestamp

5/14/2018, 2:59:07 AM

Confirmations

4,184,062

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

78842a5aaeb660db8f465988ef1f6740e2302c0212e1f2c468d0660424e75970
Transactions (2)
Coinbase61a7e403fddc57…258e2d9ace2631
1 in β†’ 1 out7.3800 XPM110 B
Adqah8zh…1WwoHJ9t
6807fe3c817e21…191b6846a864f2
6 in β†’ 2 out87.8079 XPM965 B
AdepddBi…eU9B97ytAYrvFTc2…KnLEpiCL
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.

7.670 Γ— 10⁹⁢(97-digit number)
76709673575900002258…71658605895662333439
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
7.670 Γ— 10⁹⁢(97-digit number)
76709673575900002258…71658605895662333439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.670 Γ— 10⁹⁢(97-digit number)
76709673575900002258…71658605895662333441
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
1.534 Γ— 10⁹⁷(98-digit number)
15341934715180000451…43317211791324666879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.534 Γ— 10⁹⁷(98-digit number)
15341934715180000451…43317211791324666881
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
3.068 Γ— 10⁹⁷(98-digit number)
30683869430360000903…86634423582649333759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.068 Γ— 10⁹⁷(98-digit number)
30683869430360000903…86634423582649333761
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
6.136 Γ— 10⁹⁷(98-digit number)
61367738860720001806…73268847165298667519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.136 Γ— 10⁹⁷(98-digit number)
61367738860720001806…73268847165298667521
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
1.227 Γ— 10⁹⁸(99-digit number)
12273547772144000361…46537694330597335039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.227 Γ— 10⁹⁸(99-digit number)
12273547772144000361…46537694330597335041
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
2.454 Γ— 10⁹⁸(99-digit number)
24547095544288000722…93075388661194670079
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:57,997,311 XPMΒ·at block #6,844,116 Β· updates every 60s
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