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Block #335,119

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/29/2013, 11:31:14 PM Β· Difficulty 10.1591 Β· 6,474,831 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bf5eda375073c492561e999444d007082584f236ab3aead9d98b6561b12b774b
View on Chainz β†—

Height

#335,119

Difficulty

10.159083

Transactions

2

Size

1.83 KB

Version

2

Bits

0a28b9a4

Nonce

49,984

Timestamp

12/29/2013, 11:31:14 PM

Confirmations

6,474,831

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7efccf36ec7b13803b2f65207aa5d68482693e3dcc24c5c1997a07e255b4a687
Transactions (2)
Coinbase0e650c65e234c9…f563f201b359e4
1 in β†’ 1 out9.6900 XPM110 B
AeKNrjNj…1NEq95Ta
f10a4bdb3921b7…a611a8b0c40e1c
11 in β†’ 1 out30.3574 XPM1.63 KB
AcmNSgfj…YFvs8RwQ
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.

1.031 Γ— 10⁹⁷(98-digit number)
10319376130486145494…98202309093929204479
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
1.031 Γ— 10⁹⁷(98-digit number)
10319376130486145494…98202309093929204479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.031 Γ— 10⁹⁷(98-digit number)
10319376130486145494…98202309093929204481
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
2.063 Γ— 10⁹⁷(98-digit number)
20638752260972290988…96404618187858408959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.063 Γ— 10⁹⁷(98-digit number)
20638752260972290988…96404618187858408961
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
4.127 Γ— 10⁹⁷(98-digit number)
41277504521944581977…92809236375716817919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.127 Γ— 10⁹⁷(98-digit number)
41277504521944581977…92809236375716817921
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
8.255 Γ— 10⁹⁷(98-digit number)
82555009043889163954…85618472751433635839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.255 Γ— 10⁹⁷(98-digit number)
82555009043889163954…85618472751433635841
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
1.651 Γ— 10⁹⁸(99-digit number)
16511001808777832790…71236945502867271679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.651 Γ— 10⁹⁸(99-digit number)
16511001808777832790…71236945502867271681
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:57,723,681 XPMΒ·at block #6,809,949 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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