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Block #2,637,247

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 9:03:02 PM Β· Difficulty 11.4290 Β· 4,201,924 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2bdafb68a5bdb14233e108759d024cab69e52968d1d6df31f7b3a18e40c7cc1f
View on Chainz β†—

Height

#2,637,247

Difficulty

11.428979

Transactions

2

Size

573 B

Version

2

Bits

0b6dd193

Nonce

235,525,152

Timestamp

4/29/2018, 9:03:02 PM

Confirmations

4,201,924

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

8a145fec1cacddf79a1b8bbf662e4275732cb865c0195b340ff4e1e3af83d312
Transactions (2)
Coinbase86b1cf18ccb0d0…e78f3df20f37fd
1 in β†’ 1 out7.6500 XPM109 B
Adqah8zh…1WwoHJ9t
c093853933ae70…77d3039bc65f58
2 in β†’ 2 out56.9850 XPM374 B
AcLQgjBi…LvJ2qBiwAahYoALp…A9oMoEQY
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.

6.459 Γ— 10⁹⁴(95-digit number)
64597433770138800737…73609326465399121679
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
6.459 Γ— 10⁹⁴(95-digit number)
64597433770138800737…73609326465399121679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.459 Γ— 10⁹⁴(95-digit number)
64597433770138800737…73609326465399121681
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
1.291 Γ— 10⁹⁡(96-digit number)
12919486754027760147…47218652930798243359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.291 Γ— 10⁹⁡(96-digit number)
12919486754027760147…47218652930798243361
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
2.583 Γ— 10⁹⁡(96-digit number)
25838973508055520294…94437305861596486719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.583 Γ— 10⁹⁡(96-digit number)
25838973508055520294…94437305861596486721
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
5.167 Γ— 10⁹⁡(96-digit number)
51677947016111040589…88874611723192973439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.167 Γ— 10⁹⁡(96-digit number)
51677947016111040589…88874611723192973441
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
1.033 Γ— 10⁹⁢(97-digit number)
10335589403222208117…77749223446385946879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.033 Γ— 10⁹⁢(97-digit number)
10335589403222208117…77749223446385946881
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
2.067 Γ— 10⁹⁢(97-digit number)
20671178806444416235…55498446892771893759
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:57,957,649 XPMΒ·at block #6,839,170 Β· updates every 60s
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