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Block #1,371,784

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 5:56:28 PM Β· Difficulty 10.8105 Β· 5,467,492 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
55f6c5805a2e247823d4786a9467227ab20467d5f9f3e56cff6b78a8f69c0344
View on Chainz β†—

Height

#1,371,784

Difficulty

10.810548

Transactions

1

Size

200 B

Version

2

Bits

0acf8010

Nonce

1,790,883,479

Timestamp

12/16/2015, 5:56:28 PM

Confirmations

5,467,492

Mined by

⛏️ P2SHARsQMe9NYdXrooyMHqFji6hBa75gWEtkXP

Merkle Root

58fc4c6f5b3d0fbe04599df8bf001ba49b43aaeb3c737ed004b39fea2bb56444
Transactions (1)
Coinbase58fc4c6f5b3d0f…b39fea2bb56444
1 in β†’ 1 out8.5400 XPM110 B
ARsQMe9N…5gWEtkXP
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.

1.004 Γ— 10⁹⁢(97-digit number)
10046130080032749598…40564168578830019199
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
1.004 Γ— 10⁹⁢(97-digit number)
10046130080032749598…40564168578830019199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.004 Γ— 10⁹⁢(97-digit number)
10046130080032749598…40564168578830019201
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
2.009 Γ— 10⁹⁢(97-digit number)
20092260160065499196…81128337157660038399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.009 Γ— 10⁹⁢(97-digit number)
20092260160065499196…81128337157660038401
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
4.018 Γ— 10⁹⁢(97-digit number)
40184520320130998393…62256674315320076799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.018 Γ— 10⁹⁢(97-digit number)
40184520320130998393…62256674315320076801
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
8.036 Γ— 10⁹⁢(97-digit number)
80369040640261996786…24513348630640153599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.036 Γ— 10⁹⁢(97-digit number)
80369040640261996786…24513348630640153601
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
1.607 Γ— 10⁹⁷(98-digit number)
16073808128052399357…49026697261280307199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.607 Γ— 10⁹⁷(98-digit number)
16073808128052399357…49026697261280307201
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:57,958,493 XPMΒ·at block #6,839,275 Β· updates every 60s
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