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Block #1,371,765

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 5:31:26 PM Β· Difficulty 10.8108 Β· 5,470,263 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dda484ffaa18c87c134464db7beb2328d3543cc7a1d0727c5dc369c3a8db2686
View on Chainz β†—

Height

#1,371,765

Difficulty

10.810753

Transactions

1

Size

201 B

Version

2

Bits

0acf8d85

Nonce

2,040,581,598

Timestamp

12/16/2015, 5:31:26 PM

Confirmations

5,470,263

Mined by

⛏️ P2SHAdDiSnksyGPAf52XK4EuSp4RonogLkgTRg

Merkle Root

dfa0b2c19da221b2add6dc161669d72ed6b9446b467b7db51c5e1e26180c88ee
Transactions (1)
Coinbasedfa0b2c19da221…5e1e26180c88ee
1 in β†’ 1 out8.5400 XPM110 B
AdDiSnks…ogLkgTRg
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.

4.946 Γ— 10⁹⁢(97-digit number)
49462464337609172322…23174940929060823039
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
4.946 Γ— 10⁹⁢(97-digit number)
49462464337609172322…23174940929060823039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.946 Γ— 10⁹⁢(97-digit number)
49462464337609172322…23174940929060823041
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
9.892 Γ— 10⁹⁢(97-digit number)
98924928675218344644…46349881858121646079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.892 Γ— 10⁹⁢(97-digit number)
98924928675218344644…46349881858121646081
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
1.978 Γ— 10⁹⁷(98-digit number)
19784985735043668928…92699763716243292159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.978 Γ— 10⁹⁷(98-digit number)
19784985735043668928…92699763716243292161
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
3.956 Γ— 10⁹⁷(98-digit number)
39569971470087337857…85399527432486584319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.956 Γ— 10⁹⁷(98-digit number)
39569971470087337857…85399527432486584321
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
7.913 Γ— 10⁹⁷(98-digit number)
79139942940174675715…70799054864973168639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.913 Γ— 10⁹⁷(98-digit number)
79139942940174675715…70799054864973168641
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:57,980,610 XPMΒ·at block #6,842,027 Β· updates every 60s
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